Applications have risen - as has graduate unemployment
The first figures on the numbers applying for UK university places next year shows a 12% increase on this year.
Admissions service Ucas said it was likely that, once again, competition for places was likely to be strong.
The figures relate to the first, October deadline - for places on medicine and veterinary courses and at Oxbridge.
They show the total number of applicants has gone up from 64,438 at this time last year to 71,883.
There have been 27,429 applicants for medicine courses, up 13.7%.
Dentistry courses attracted 12.6% more applicants - 3,720 in total, and veterinary medicine 14% more: 2,320.
The total who have applied so far for all other courses - including those at Oxford and Cambridge - was 44,454, which was 11.6% more than last year at this point in the applications cycle.
The number of applicants from outside the UK was up 16.6% - notably from Ireland (up 43%) and from China (27%).
Ucas' acting chief executive Virginia Isaac said it was too early in the 2010 entry cycle to tell whether the significant increase in applicants would be sustained throughout the process.
"It does indicate, however, that in certain areas, once again, prospective students will be facing strong competition for places," she said.
The executive director of the 1994 Group of research-intensive universities, Paul Marshall, said the rise was proof that universities' efforts to encourage participation in higher education were working well.
"1994 Group universities want to help meet this healthy demand but we must all recognise the financial pressures universities are under to maintain the quality of student experience," he said.
"Any further expansion must be fully funded so that universities can continue to develop the very best graduates and offer a world class academic experience in a research rich environment."
Last year the government belatedly made extra places available but only on certain courses - and did not fully fund these.
Ucas statistics show that the number of students who took up a place at university this autumn was 6% higher than in 2008. The number who had applied had been about 10% higher.
The shadow universities and skills secretary, David Willetts, said: "Ministers are sleepwalking into another university entrance crisis.
"This year, far more potential students than usual have been left without a place and we can now see the problems are set to be even worse next year.
"It was obvious from the demographics and the state of the economy that more people would aspire to go to university.
"Ministers failed to tackle the issue in 2009 and are now repeating their mistakes for 2010."
Meanwhile graduate unemployment went up by 44% in the past year to its highest rate for 12 years, according to the Higher Education Careers Services Unit.
It said almost 8% of those who left university in 2008 were out of work in January compared with 5.5% a year earlier - and things could get worse.
But the unit's chief executive, Mike Hill, said: "Graduates shouldn't feel disheartened: many organisations continue to recruit and a degree will certainly remain valuable for many years to come."