The government should slash student places at "pile it high, sell it cheap" universities – even if it means some being forced to close – to protect Britain's "world class" research institutions, the head of University College London has said.

Speaking ahead of a speech on Thursday by the business secretary, Vince Cable, in which the government is expected to outline plans to cut costs in higher education, UCL's Malcolm Grant said elite universities feared the government was poised to cut research funding.

Such a move could "decimate Britain's global competitiveness in research", Grant told the Guardian, arguing that there is a "direct human benefit" in areas such as cancer and Parkinson's disease from research-intensive universities.

Grant, provost of UCL – rated fourth best university in the world after Harvard, Cambridge and Yale – said: "The biggest risk to the big research universities is a cut in funding for research, if that was done without proper identification of excellence then it would decimate Britain's global competitiveness in research."

As applications for university places continue to soar – they hit a record high for the fourth year in a row – the government is under intense pressure not to impose further cuts on the numbers of students.

Cuts in teaching budgets would affect all universities and risk protest from the families of bright children who were denied places. But cutting research funding would hit elite universities disproportionately; last year UCL received nearly £69m from the government for teaching compared with £104m for research.

Grant said: "The politics of reducing total student numbers is very difficult, if it then leads to the conclusion that there should be fewer universities. There will be political pressure to keep open universities at the teaching-only end of the spectrum by taking resources away from the world-class research universities."

David Willetts, the universities secretary, has hinted that students could soon be forced to pay higher tuition fees, warning that the cost of degree courses was a "burden on the taxpayer" that had to be tackled.

But in return, universities will come under pressure to improve the quality of their teaching and ensure that students are prepared to enter a tough jobs market.

Last month, Willetts told the Guardian: "The system doesn't contain strong incentives for universities to focus on teaching and the student experience as opposed to research."

Grant urged the government to consider reducing student numbers if that was the price of maintaining Britain's research heritage. "I think it's an avoidable consequence if politicians are prepared to revisit the question of student numbers," he said.

UCL researchers work on conditions ranging from cardiovascular disease to MRSA; an ex-PhD student, Charles Kao, won the Nobel prize for physics in 2009 for work on fibre-optic communications.

Grant said: "If you talk about research, people don't realise what huge human benefit, direct human benefit, comes from it. We've got a major cancer unit, we've got people working on Parkinson's, we've had the award of a Nobel prize."

Grant said differences between universities were not reflected in the fact that all of them charged the same tuition fees. This masked the fact that elite universities offered a far richer experience, he said

"Universities vary quite a lot in the cost of their teaching, but you can't vary the price. Much of it depends on whether you're a research institution, whether you've got libraries or 'pile it high and sell it cheap' – these differences aren't reflected in the funding model."

The elite Russell group of universities are keen to allow institutions to set their own fees – they have argued in their submission to Lord Browne's review of fees that students who stand to gain the most should pay the most.

Grant said that if the government favoured an increase in tuition fees, the cost of a UCL degree could rise towards the amount charged to a foreign student.

According to next year's fees schedule, an arts degree such as ancient history will cost £12,770 for an overseas student while medicine will cost £24,940.

He said, however, that fees charged to domestic students would always be lower than those to foreign students because of the taxpayer subsidy – and there would not be a variable cost by subject to avoid deterring applicants for the sciences, which cost more to teach.

Grant said he aspired to the Yale model, in which students are charged a headline fee of $51,000 (£34,000), but only half of them pay the full amount. However, British universities lack the generous endowments make the American system of bursaries possible. Britain is "light years" away from that, he said.

Pam Tatlow, chief executive of million+, which represents many of Britain's new universities, said the UCL head's view "fails to recognise that our higher education sector must deliver results for universities, students, the UK economy and society rather than just a handful of vested interests." He urged the government to maintain the number of student places: "Coalition ministers would be extremely short-sighted if they paid any attention to these suggestions and supported a very small number of universities at the expense of providing places for the record numbers of applicants hoping to secure a place at university in this or future years. They would also be breaking the commitment to social mobility made in their coalition agreement only a few weeks ago."

To help prepare students for a demanding global jobs market, UCL is planning to introduce a combined honours degree in arts and sciences. The interdisciplinary degrees will include optional modules from across the range of subjects in science, culture and health. Such degrees are regarded as challenging and aimed at the most able students.

A government spokesman said the business secretary's speech had not been finalised. However, Cable is expected to say costs could be reduced by separating teaching from examining, so that new institutions would be allowed to teach students for degrees that would be awarded by more prestigious universities. He is keen to encourage the growth of private universities. He has also agreed that Labour's plan for half the population to go to university should be scrapped.