Planned cuts in funding pose a risk to the world-class standing of English universities and threaten the country's future prosperity, the head of the group which represents vice-chancellors warns today.

Universities face the deepest cuts of any publicly funded activity, ushering in the most radical changes to higher education in five decades, which could see the closure of "swaths of institutions", says Steve Smith, president of Universities UK and vice-chancellor of Exeter university.

Lord Browne's review of university finance, published last week, assumed the teaching budget would be cut to £700m with funding concentrated in priority areas such as medicine and engineering.

In Education Guardian, Smith writes: "The state is essentially withdrawing from funding university teaching except in a small number of 'priority' subject areas."

Universities will also be hit by cuts to government funding for scientific research. In total, budgets for universities and research could lose £4bn-5bn from a current funding level of about £11.5bn, Smith writes.

"These are unprecedented cuts in state funding to universities, and I doubt any other area of publicly funded activity will fare as badly in the spending review."

Smith sent an email to vice-chancellors last week in which he warned universities to expect an 80% cut to teaching budgets. He warned that if parliament refuses to pass Browne's recommendation to raise tuition fees, universities will not be able to replace the shortfall.

In today's article he writes: "The government should be in no doubt about the risks these cuts in funding pose to the world-class standing of our higher education system, and thus to the country's future economic growth and prosperity.

"The UK's competitors face the same deficit reduction challenges as we do, but they have decided to invest in higher education at this crucial time, not cut it."

Smith warns that however the cuts are implemented "one inevitable result will be the removal of swaths of institutions and departments".

It was reported at the weekend that Cambridge University is drawing up plans to go private because proposed rises to tuition fees do not go far enough to enable it to compete with the US Ivy League. This was dismissed as "complete speculation" by a university spokesman yesterday.

However, some of Britain's leading universities are concerned they may not be able to – and crucially, may not wish to – raise their fees to the high levels necessary to make up shortfalls in funding from cuts imposed in the spending review.

Malcolm Grant, head of UCL, said in a recent blogpost that Browne's proposals may not help "globally competitive" universities because of the government levy imposed on fees above £6,000.

Grant wrote: "The headline message is that the cap on fees is to be lifted. The reality is that this is will not significantly advantage leading universities."

The levy may even operate as a "perverse incentive" for some universities to concentrate on increasing foreign student numbers at the expense of places for UK undergraduates, Grant wrote. International students can be charged high fees without a levy.

Browne's proposals have also been criticised by the university lobby group Million+, which represents 28 former polytechnics.

In a briefing to MPs, Pam Tatlow, the group's chief executive, writes that universities will have to charge more, but will be worse off financially.

"Whether they like it or not, universities will have no option but to charge students much higher fees to make up for the shortfall in funding."

"MPs will have to defend much higher fees on the doorstep, not because more investment is being provided for universities or to improve the student experience, but because the Treasury decided to cut the deficit by cutting the public funding of higher education.

Universities and Science minister David Willetts said the vice-chancellor's comment piece painted "too bleak a picture".

He said: "We will continue to fund higher education but by putting the money directly in the hands of students. We will lend them the money to pay for their course … support students with maintenance grants and continue funding high-quality research."