Leading institutions will be forced to close their doors to increasing numbers of outstanding candidates next year.
Cambridge University had 13,700 applications for 3,400 places last year.
And now the university is bracing itself for the "2005 effect". Up to 100,000 more students are expected to apply to universities nationally as gap-year students rush to start courses before the 2006 introduction of top-up tuition fees. At the same time, more students from a larger 18 to 21 population cohort will pass A levels and thousands of hopefuls from the ten new European Union countries move will be able to benefit from the UK higher education system.
"We are very concerned and have written to the government about this," said Geoff Parks, Cambridge's director of admissions. "Those who would have got a place here if applications had been steady will now be disappointed."
No one is quite sure how many prospective gap-year students will try to escape the 2006 fee regime, which will see top-up fees of up to £9,000 over three years. This is compared with just over £1,000 a year fees for those joining in 2005, who will also enjoy deferred payments in 2006 and 2007.
As many as 100,000 students take a gap year every year. Research by the Liberal Democrats earlier this year found that 67 per cent of potential gap-year students will abandon their plans - equating to an additional 67,000 UK students competing for degree places - to beat fees.
But the government is keen to tone down such estimates. The Department for Education and Skills argued that many gap-year students would prefer to start courses in 2006. All students will pay their fees only after graduation, when their salaries reach £15,000. Poorer students will benefit from the reintroduction of grants worth up to £2,700 a year and from bursary schemes.
"Many students will balance these benefits with the benefits of taking a gap year and make a well-informed decision about whether it suits them or not," a spokeswoman said.
Gordon Brown, the chancellor, announced in February that working-class teenagers who did voluntary work during a gap year would be given help with living expenses and future college fees.
But experts warned that the government's message was not getting through to students.
Dr Parks said: "We have seen about 11,000 sixthformers at access events this year and none of the kids we spoke to are contemplating taking a gap year as they want to get in before 2006."
Dr Parks said there was also concern about an increase in the number of applicants from the European Union, as students from the ten EU accession countries will now pay the same fees as home students.
The Higher Education Policy Institute last month predicted that the number of undergraduates from countries such as Poland, Hungary and the Czech Republic could increase to 30,000 by 2010, with most of the increase coming immediately in September 2004, for 2005 entry.
In an earlier report, the institute also warned that there would be a demand for an additional 150,000 undergraduate places by 2010 purely as a result of general population growth combined with higher A-level pass rates.
Barry Taylor, Bristol University's communications director, said: "There is already fierce competition for places in a small number of the subjects we offer, and we are concerned that more of the outstanding candidates who apply to Bristol may have to be disappointed."
Anthony McClaran, chief executive of the Universities and Colleges Admissions Service, said that it was too early to predict the increase in numbers, but that increased entry requirements and a greater reliance on the clearing system could be expected.
Durham University is also bracing itself. "It is going to be a bumper year for university applications in 2005," Matthew Andrews, head of admissions at Durham and a lead member of the University Admissions Practitioners Group, said.
He said that Durham had already started to raise its entry requirements to reflect increased competition for places, but not in specific reaction to the expected 2005 rush.