Thousands of university places could be left unfilled and institutions millions of pounds out of pocket, because high fee-paying international students are being blocked from starting degrees under a new visa system, vice-chancellors warned yesterday.

Universities fear wealthy foreigners, who can pay more than £20,000 a year for degree courses, according to data compiled for the Guardian, will be put off studying in Britain by massive delays in processing visa applications, prompting a funding crisis. In Pakistan alone, a backlog of 14,000 applications has caused havoc for students who had been due to start courses this term.

Universities UK (UUK), the vice-chancellors' umbrella body, said it was likely that within weeks it would be too late for students to start their courses, and institutions would have to ask them to defer for a year.

Some universities have started filming lectures so students unable to get into the UK can catch up by watching them online if they finally get here. Others have suggested providing reading materials so they can start at home. But it is thought that many will close their doors to delayed entrants around the start of November.

Such a move would cause huge administrative headaches, not just for disappointed students but also for institutions who will then have unexpected spare places this year, but will have to take deferred students next year, putting pressure on 2010 admissions.

Income from foreign students is crucial to UK universities because they face a cap on the number of British and European students they can take. Home and EU students pay tuition fees of up to £3,225 a year but the cost of educating them is much more and is supplemented in part by the government, which therefore limits places for them.

Professor Steve Smith, the president of UUK, which is in talks with the UK Borders Agency to try to speed up the visa process, said: "We are very concerned that significant numbers of students from Pakistan may not receive their visas in time to start their studies in the UK this year.

"Universities UK has consistently emphasised to UKBA that international students only have a limited timeframe within which to apply for a visa and any delays are very serious.

"We know many universities are trying to accommodate late arrivals but there will be cut-off points after which students will not be able to join their programmes. This is obviously devastating for the students and problematic for institutions who have planned for certain student numbers.

"It is of huge academic, cultural and financial benefit to the UK for these highly-talented people to come to our country to be educated. We are in danger of sending out a message that the UK does not welcome international students."

Overseas students contribute £4bn a year in fees, according to the UK Council for International Student Affairs (Ukcisa). The Higher Education Statistics Agency says more than 8% of the total income of UK universities comes from international students' fees.

Data gathered for the Guardian by Mike Reddin, a former academic at the London School of Economics, shows that students from outside the European Union starting undergraduate degrees in the sciences at Imperial College London this autumn will pay up to £20,400 each year in fees.

International students on a undergraduate science course will pay an average of £10,781 each year, a 3.7% increase on last year's fees. For arts courses, the figure is £9,911 - up 4.2%. Dominic Scott, Ukcisa's chief executive, said the figures showed just how important international student fees were to the UK.

"Without it, universities would have more departments closing, worse infrastructure and less investment in libraries," he said. "At a time of huge financial pressure, it is the international student income which is enabling universities to invest, expand and survive."

At the London School of Economics, where a large proportion of undergraduates come from outside the UK and EU, Simeon Underwood, head of admissions policy said significant numbers of students were arriving later than usual, and some had not come at all.

"The sector's main worry is the damage this will do to the reputation of UK higher education overseas, especially in the Indian sub-continent, and the knock-on effect this will have on university funding," he said.