Vice-chancellors are set to urge the government to scrap its commitment to increase the number of student places allocated to the cheapest institutions.

Ministers should also review their timetable for reducing the AAB A-level threshold for unlimited competition for students, according to a draft version of Universities UK's submission to the White Paper consultation.

The document, discussed last week at UUK's annual conference, warns that the government's current proposals risk "undermining the diversity of excellence across the sector", could reduce opportunities for students and may curtail social mobility.

It points out that a "key risk" of the plans is a cut in the number of places for qualified students "at the universities they want to attend".

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This is a clear nod to the effect of deducting 8 per cent of non-AAB places from each English university and offering the resulting 20,000-strong group to institutions charging less than ?7,500, such as further education colleges and private providers.

"It is not clear that the expansion of the current price-related margin will help the government meet its goal of a student-centred system," the draft document states.

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The strong language reflects growing unease among vice-chancellors over the number of places they will lose to the price margin - and how many more they stand to lose in 2013-14 if the scheme is extended.

In his speech to the conference, Vince Cable, the business secretary, said: "We want to increase year on year the number of places that are liberated from number controls. We want the 20,000 places for which institutions will need to compete to grow, to expand," he said.

That could leave some universities losing hundreds of places in successive years unless they reduce their undergraduate tuition fees.

It has already emerged that around 12 universities have contacted the Office for Fair Access about reducing their fees for 2012-13, but it is understood that "many more" are privately considering a cut to enable them to bid for the marginal places.

Eric Thomas, the new president of UUK and vice-chancellor of the University of Bristol, indicated that ministers would be urged to revisit the idea of taking bursaries into account when calculating average fees, thereby allowing more institutions to drop below the ?7,500 threshold.

"Many of my colleagues think we should factor in bursaries because that is still creating financial headroom for students ... but on something that many people argue is more directly important (than fee waivers) during your time at university," he said.

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Cable the conciliator

Elsewhere in his speech, Mr Cable struck a more diplomatic tone with the sector in an apparent attempt to build bridges with vice-chancellors, who have been critical of his approach since he took office.

He admitted that the past year had been "at times traumatic" and also made reference to his own time as an academic about 40 years ago, which some have claimed may have given him the wrong impression of present-day higher education.

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"It is important that I don't get trapped in the mental pictures and prejudices that I picked up through those experiences," Mr Cable said.

On some aspects of policy, he also appeared willing to take criticism on board. He accepted that the AAB plans on their own could have a negative impact on social mobility.

But he insisted that they would be "more than neutralised" by the government's "massive concentration" on admission for poorer students through access agreements.

"If all other things were equal, then simply freeing up the AAB process might (affect fair access), but it is not the only thing we are doing," he said.

Meanwhile, the UUK conference, held at Royal Holloway, University of London from 6 to 8 September, also heard from former Labour minister Alan Milburn, the coalition government's independent reviewer of social mobility.

He urged more use of contextual data to aid the admission of those from poorer backgrounds - a method that some sector observers say will be undermined by the AAB plans.

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simon.baker@tsleducation.com.