Roshonara Choudhry was a star student. Despite a disadvantaged background as the daughter of Bangladeshi immigrants, both of whom were unemployed and living on benefits, she secured a place to study English and communications at King's College London. After two years of study, Choudhry, who was fluent in four languages, was predicted to get a first.

But then, in early 2010, the 21-year-old dropped out of her course. After leaving her home on 14 May, she paid off her student loan (partially with academic prize money), emptied out her bank accounts, and attempted to stab Labour MP Stephen Timms to death because he had voted for the war in Iraq. She had come under the influence of an al-Qaeda leader sermonising online. In November, she was sentenced to life in jail.

To what extent are British universities breeding grounds for Islamic radicalism? Can our institutions do more to control extremist activities on their campuses, and prevent extremist ideologies from spreading to students? Or is it simply not their responsibility to address the problem in the first place - and possibly even antithetical to their mission?

These questions are very much on the agenda, with a Universities UK report on how universities can "best protect and promote freedom of speech and academic freedom, whilst taking appropriate action to prevent violent extremism" due later this month. The working group was set up exactly one year ago, after Umar Farouk Abdulmutallab was arrested in the US on Christmas Day 2009 for attempting to blow up a US aeroplane with 289 people on board. He studied for an undergraduate degree in engineering and business finance at University College London between 2005 and 2008.

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According to another report prompted by his arrest, Radical Islam on UK Campuses: A Comprehensive List of Extremist Speakers at UK Universities by The Centre for Social Cohesion (CSC), he was far from the first UK student to be involved in terror activities.

"For many years," argues Douglas Murray, director of the CSC, in the report's preface, "it has been clear that British university campuses are breeding grounds of Islamic extremism. Omar Sheikh was radicalised in the 1990s while studying at the London School of Economics" and was eventually sentenced to death in Pakistan in 2002 for the killing of journalist Daniel Pearl. In 2003, two undergraduates from King's College London went to Israel and carried out a suicide-bomb attack in a bar in Tel Aviv.

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There is obviously room for dispute about how and where particular individuals were radicalised. Nonetheless, the CSC report could point to 19 people who had studied at British universities (before Abdulmutallab) and "have committed acts of terrorism or have been convicted for terrorism-related offences, in the UK and abroad". Four had held senior positions in university Islamic societies (ISocs) and six were still students at the time of their arrest. A wide range of different institutions were involved.

Two of those convicted of conspiracy to cause explosions in the "dirty bomb" plot in 2004, which targeted financial institutions and the London Underground, were studying at Brunel University and the University of Westminster. The "fertiliser bomb" plot in 2005, aimed at shopping centres and nightclubs, also involved students and former students from Brunel and the University of East London.

One of those convicted of the "transatlantic liquid bomb" plot in 2006 had been president of London Metropolitan University's ISoc. The man who died after driving a burning Jeep packed with explosives into Glasgow airport in 2007 had studied at Anglia Ruskin University before serving on the executive of the ISoc at Queen's University Belfast. Others charged with a variety of offences included a president of the ISoc at the University of Westminster's Harrow campus, someone who was running the website of the University of Leicester's ISoc, as well as students at the University of Brighton, Glasgow Metropolitan College, the University of Humberside (now part of the University of Lincoln) and University College London.

More recently, MI5 identified 39 (unnamed) universities as being "vulnerable to violent extremism". All have been briefed by the Joint Terrorism Analysis Centre and offered money for the specific purpose of addressing radicalisation on campus. It is known that both the University of East London and Birmingham Metropolitan College accepted funding under a similar scheme that was put in place last year.

And, most recently, the man who blew himself up in Stockholm in mid-December, injuring two, had studied at Luton University, now the University of Bedfordshire.

For Lucy James, a research Fellow at the Quilliam Foundation, "the world's first counter-extremism think-tank", universities are "absolutely critical" to the spread of Islamic extremism in Britain.

"It's not a 'what if' situation," she says. "We've already seen four former senior figures in university Islamic societies convicted of terrorist-related offences, with another on trial for the Christmas Day attempted bombing.

"Things are getting worse and universities have done little or nothing. They seem disinclined to acknowledge the problem, because it's complex, and feel the need to cherish freedom of speech. If you try to bring the issue up, you get Milton quoted at you.

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"People don't see the danger of non-violent Islamism. Yet as well as possibly leading to terrorism, it is also very bad for cohesion on campuses."

Raheem Kassam, national director of Student Rights - which was set up in 2009, he says, "in response to students' anger at disruption to their lives" - prefers to speak of "Islamism" rather than "Islamic extremism". Although his organisation is "opposed to all forms of abuse on campus", it is the Islamic variety that "comes up most often and leaves the clearest paper trail, since the events are openly advertised".

"Much of the rhetoric coming from vice-chancellors is dismissive and therefore dangerous, because they don't want to acknowledge that extremism is a problem on their campus," he says.

"Not every student is a radical, not every radical is an extremist and not every extremist is a terrorist," reflects Anthony Glees, director of the Centre for Security and Intelligence Studies at the University of Buckingham. "But every terrorist is an extremist, a radical, and some of them, alas, have also been students."

There is no doubt that the precise process of "radicalisation" remains mysterious.

"We know that when people are confronted with extremist ideas," explains Glees, "some will reject them, some will find them attractive and some will act them out."

But, he continues, that is no reason to deny that radicalisation can occur, not least on university campuses, that it can occasionally lead to "terrorism and killing people" and that we are witnessing "a failure on the part of higher education institutions to realise what is happening under their noses, on their watch and in their time".

Much of this is inevitably disputed: whether "radicalisation" is a useful term, how it develops and how much of it is taking place within universities. But although the debate can get pretty rarefied, two recent reports bring the opposite approaches into sharp relief.

Umar Farouk Abdulmutallab: Report to UCL Council of Independent Inquiry Panel, also known as the Caldicott report, examines the case of the former student and president of the ISoc at UCL.

The report makes a number of concessions. It acknowledges that the academic staff in his department of mechanical engineering were "not aware that Mr Abdulmutallab was President of the UCLU ISoc". It admits that a number of meetings involving speakers invited by the ISoc who were "controversial and potentially a focus for protest" had to be cancelled, albeit on health and safety grounds. It implies that lessons have been learned, as reflected in some proposed measures that "in combination, may reduce the future risk of students being radicalised and increase the university's ability to identify any student in the process of radicalisation".

It also notes two depressing precursors to the Abdulmutallab case: Samar Alami, who got a first degree and a master's from UCL, served as president of the student Palestinian Society and was later convicted of detonating a car bomb outside the Israeli embassy in London and sentenced to 20 years in prison; and Mohammed Abushamma, who enrolled for a BSc in natural science at UCL in September 2008, after he had already been arrested, and went on to plead guilty to preparing acts of terrorism. In June 2009 he was sentenced to three years in prison.

Yet ultimately, the UCL report concludes that "there is no evidence to suggest either that Umar Farouk Abdulmutallab was radicalised while a student at UCL, or that conditions at UCL during that time or subsequently are conducive to the radicalisation of students".

Furthermore, it makes a point of stating that the measures it recommends "will clearly not eliminate the risk of radicalisation of UCL students. We consider that is an unrealistic aim without changing UCL's fundamental mission and character."

This gets to the heart of the issue. Terrorism came almost to the door of UCL in 2005, when the blast from the bus blown up in nearby Tavistock Square on 7 July not only killed one of their employees but was clearly audible on campus. Abdulmutallab's radicalisation, wherever it occurred, is alleged to have almost led to an even more appalling terrorist atrocity. Yet instead of proclaiming that it will strain every sinew (or some similar cliche) to prevent anything like that happening again, the report specifically says that "UCL's fundamental mission and character" inevitably brings risks. Is this just a realistic acknowledgement that nothing in life is risk free? Or is it a failure of responsibility?

The report came in for much criticism as a "whitewash", with columnist Nick Cohen referring to "the limitless capacity for self-delusion of British academe". Some noted that the panel had consulted many people within UCL but few who could have shed further light on Abdulmutallab's views and activities while a student - especially given that Alan Johnson, the home secretary at the time, told Parliament on 5 January 2010 that between 2005 and 2008, Abdulmutallab was known to the Security Service, MI5. It was also observed that, after giving itself a clean bill of health, UCL seemed to be recommending a rather extensive range of reforms to its procedures.

In response, one member of the inquiry panel, Ruth Siddall, UCL's dean of students (welfare), was adamant that the university had done enough. "Our heads of security have close relations with the police, but we were not aware of Abdulmutallab being surveyed," she says. "Any concerns were not being conveyed to us. He was an average student, well integrated, and played football before or after Friday prayers. He may have been committed to a very strict and traditionalist form of Islam, but he was not a firebrand or a campaigning president.

"We have looked and haven't found any sign of radicalisation within the UCL ISoc - I'm not going to make things up. They operate openly and anyone can go to their meetings. They are not operating behind closed doors to a restricted audience. I'm worried about the assumption that all Islamic societies are the problem.

"We are not able to control what a student is looking at on the internet and we shouldn't be spying. It's not the job of a university to monitor what students or staff are doing in their spare time. I believe we don't have a problem or a case to answer, but there's no room for complacency. Vigilance should also enhance the student experience," Siddall says.

A very different picture emerges from Radicalisation on British University Campuses: A Case Study, a recent briefing paper James produced for Quilliam. After starting with a reference to UCL, this focuses on City University London, where "the head of another ISoc and his followers praised Anwar al-Awlaki, Abdulmutallab's al-Qaeda supporting mentor, called for 'offensive' and 'defensive' jihad, advocated the murder of homosexuals and non-practising Muslims, and set their own ISoc on a collision course with the university authorities, staff and other students".

Much of the material comes from the khutbahs, or Friday sermons, uploaded on to the ISoc's website.

The paper tracks "a real-life, recent example of how extremists can take control of an ISoc" and "the shift from an intolerant and highly politicised - though non-violent - version of Islam, to one that legitimises and encourages violent action".

"Just as it is right to be concerned about the danger of fascist rhetoric spilling over into violence," claims James, "so it is right to be aware that extreme forms of Islamism may potentially provide a launch pad for Islamist-inspired terrorism."

Yet over and above the creation of "a more dangerous atmosphere in which radicalisation towards terrorism has a greater potential to occur", the paper examines the effect on campus of the promotion of an ideology "that impacted on, and was intolerant of, members of other faith groups, those with alternative sexual orientations and women". Women, Jews, gays, non-observant Muslims and those involved in student politics and journalism all reported a souring of the atmosphere at City and feelings of intimidation.

"It is clear that the ISoc's members," concludes the report, "without necessarily breaking any laws, have had a chilling effect on the academic and social life at City University (and) directly undermined two of the five key objectives put forward by the government for university campuses in 2007: 'to break down segregation amongst different student communities' and 'to ensure student safety and campuses that are free from bullying, harassment and intimidation'."

All this amounts to an appeal that "the liberal traditions of British universities are under threat and...worthy of defending".

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In the case of City, the former deputy vice-chancellor, Julius Weinberg, accepted the accuracy of the Quilliam report as a portrayal of campus life in the past academic year, although he believes that things have subsequently been put right. More generally, however, there are obvious reasons why universities are reluctant to face up to issues of extremism - it is hardly good public relations to admit it is a problem and, if you ignore it, it may go away. But does this reluctance represent a deeper intellectual failure?

"Some academics don't want to speak out," says Student Rights' Kassam, "as they are worried they would be seen as supporting a government that launched a War on Terror. This can lead to an attitude towards Muslims of 'Your frustration is understandable - have a racist outburst'. Sympathy with the grievances of British Muslims often leads to indulgence or fingers in the ears."

Glees is critical of publicly funded research that ends up "proving" that "the problems of radicalisation are of our making, rather than of our enemies". He suspects that some in British higher education "actually like the idea of its students being 'radicals'" or see radicalisation "as some kind of rite of passage that must be safeguarded if the idea of free speech is to retain its meaning. Yet in an educational setting people shouldn't be allowed to promote extremist messages - that doesn't mean they should locked up or prevented from sounding off in pubs.

"Someone in the Crown Prosecution Service made a comparison with child pornography. Just because it's out there on the internet doesn't mean it should be decriminalised. Just because extremist ideas are out there doesn't mean you have to bring them on to campus."

This applies particularly to questions of gender raised, for example, by calls for segregated meetings, since "if you don't have gender equality in education, you never have it", Glees says.

It also applies to the speakers invited to events on campus. Hannah Stuart of the Centre for Social Cohesion alleges that "some ISocs continue to give an unchallenged platform to speakers who advocate anti-Semitic, homophobic and illiberal views - or even glorify terrorism. Intolerant speakers are unfortunately commonplace. They do not represent the views of most Muslim students.

"Instead they are encouraged by the Federation of Student Islamic Societies (FOSIS), who often arrange national speaking tours, and by a handful of students who take control of ISocs to promote their own interpretation of Islam at the expense of others. Many universities have few or no procedures to regulate external speakers and some students have taken advantage of their unwillingness to recognise the problem for what it is."

In response, FOSIS president Nabil Ahmed said: "We must be responsible in understanding speech, and tolerate speech including that with which we disagree. We have a robust legal code for speech in Britain and should it be crossed, any speaker should have to answer to the law."

He added that allegations of extremism on campus have been "few and far between" and shocked Muslim students "who not only consider such actions antithetical to the most basic principles of Islam, but are once again under scrutiny for a crime they did not commit".

On a recent visit to the University of Oxford's Middle East Centre, Glees says he noticed that the forthcoming talks were on "The art of resistance in the Middle East", "The rise and fall of the global jihad: disentangling myth from reality", "Hamas and the opposition to the current Palestinian-Israeli negotiations" and "Israel and the failure of the American Jewish establishment".

"I can't say I like the sound of any of them from a radicalising point of view," he says, calling for universities to offer "a more balanced perspective, with counter-argument for every argument".

The "War on Terror" week held at UCL while Abdulmutallab was president of the ISoc or the recent "Justice" week organised by the ISoc at Imperial College London have raised similar objections. However, a spokesman for Imperial said the latter had been "considered by the college and students' union to meet the requirements set out under the college's Code of Practice on Freedom of Speech".

Although he "respects student democracy", Kassam believes there are not enough checks and balances in the booking of speakers. He calls for "balancing the panels in debates or moving events off campus, so they are not using taxpayer resources. That's much better than outright banning. We need an intelligent discourse about contentious issues alongside activism. It is the responsibility of student unions to get the best out of their debates."

In this, Kassam is strongly opposed by the authorities at UCL who refuse to operate a "no platform" policy. The recent report argues that "speakers with controversial but not illegal views were welcome to the extent that they could be expected to stimulate debate". Universities, it is implied, are precisely the right places for unpopular and even offensive opinions to be aired and challenged. It is an indication of how the issue of extremism prompts the question of what universities are for that this approach can be seen either as a shameful dereliction of duty or as part of their "fundamental mission and character".

One academic who has experienced the impact of extremist ideology first-hand warns that the UK academy may be under-equipped to even appreciate the danger of Islamism.

Mina Al-Lami, visiting Fellow in the department of media and communications at the London School of Economics, studies the Arabic-language "media and propaganda of the Islamic extremist groups affiliated or sympathetic to Al-Qaeda, the websites calling for jihad and inciting violence as the only means to achieve their goals and sometimes as an end in itself".

Although such websites are vicious about Israelis, Americans and Britons, she notes, "increasingly Shias have become the number one enemy. They legitimise the killing of Shias, both combatants and civilians, anywhere and at any time. They see the West as the biggest target but Islamic regimes and those who work for them as easier targets and more reachable."

While welcoming the fact that more Western scholars have been studying Islamic extremism and radicalisation since 9/11, Al-Lami notes that many rely on translations of the original Arabic sources and regrets that "we don't hear the voice of Arabic analysts, academics and journalists who have been following the groups for years. We know the rhetoric, the grievances and the socioeconomic factors. Familiarity with the culture and ideology puts us in a good position to know how to deal with the situation and recommend what could be done."

Al-Lami takes the material very seriously, for a number of reasons. She is herself from an Iraqi Shia background, the Arabic websites are far more vitriolic than anything available in English and groups like those she studies were responsible for the death of her brother and the persecution of her family. She fears that Western experts, by contrast, often play down the danger of jihadism and get bogged down in details of terminology.

"In academic circles," she argues, "the material can be taken too lightly, because there's a lot of political correctness, there's always a worry about Islamophobia and you sometimes get people saying that it's not really a problem, it's not as bad as the media make out, these people have the right to express their views.

"At talks and conferences, the term 'radicalisation' is seen as problematic, as a media term that demonises certain people, although we needed a term that implies a gradual process and I couldn't find another. No one came up with an alternative. Yet it almost became a taboo word," Al-Lami says.

"You can't say 'Islamic terrorism'. We get similar comments if we use the word 'jihad' - normally seen as a good thing in its original context - in a negative sense. There is a danger of getting hung up on terminology and not moving on to the things I think are more important" - for example, the reality of British university campuses that are breeding grounds for terrorism.