Only Australia will have a larger rise in international students, with an extra 50,000 by 2020, the report says.
Nearly 30,000 more international students will be enrolled on UK university courses by 2020, it adds.
India will overtake China as the leading country for sending students abroad by 2020, the report also predicts.
It currently has 39,000 students in the UK, compared to 67,000 Chinese nationals, according to the latest figures from the Higher Education Statistics Agency.
Speaking ahead of the British Council’s Going Global conference in London, which starts on 13 March, Jo Beall, the council’s director of education and society, said the UK stands to reap the rewards of a “decade of opportunity” in global higher education if it makes the right moves in developing markets around the world.
“Our study shows that the next 10 years are critical - the UK has a decade of opportunity ahead of it if its universities, colleges, business leaders and policymakers are ready to take decisive steps to engage with the global higher education market,” said Dr Beall.
“In an increasingly connected and interdependent world, a willingness and an ability to collaborate internationally and to respond to changing trends are vital.
“We cannot afford to miss out on the prospects highlighted in this report.”
In terms of the potential market for higher education, the British Council observes that just four countries will account for more than half of the world's 18 to 22-year-olds by 2020 - India, China, the US and Indonesia.
It highlights that competition for increasing numbers of globally mobile students will remain strong, especially from the US and Canada, with higher university tuition fees and tougher visa rules in the UK posing a risk to the international popularity of UK universities and colleges.
The conference – for which Times Higher Education is media partner – is being opened by Vince Cable, the business secretary.