The clearing process for students who fail to make their grades this summer will be "the most frantic and stressful in living memory", it has been claimed.
Sally Hunt, general secretary of the University and College Union (UCU), warned that "the stakes have never been higher" for applicants.
Universities have revealed that vacancies are now scarce, with most of the UK's leading Russell Group institutions having no places left on undergraduate courses.
Oxford, Cambridge, Bristol, the London School of Economics, Imperial College London, Warwick, University College London, Edinburgh and Birmingham are not entering clearing.
A survey by the Press Association of almost 60 institutions has found that more than a quarter say they will not enter the clearing process, or are highly unlikely to do so.
Clearing matches students who have not received any offers, or been turned down by their original choices due to lower than expected grades, to other available courses.
The poll paints a bleak picture for students whose results are lower than hoped, particularly those hoping to find a place at a top-flight university.
A Birmingham University spokesman said: "We may be able to take a small number of students through the national adjustment process provided they have grades of AAB or better."
Adjustment allows students to trade up if they receive better-than-expected grades.
Glasgow University also said it will not have clearing places, although there may be a very small number for courses at its Dumfries campus.
Cardiff University said it will be entering clearing, with a slightly higher number available than in previous years due to more funded places being provided by Wales' higher education funding council.
King's College London said it will have a "very limited" number of places, while Nottingham said it may have around 20.
A number of other universities are also closing their doors, including Surrey, Oxford Brookes, Chester, Leeds Metropolitan, Reading and Harper Adams University College who all said it was unlikely that they would take part in clearing.
Ms Hunt said: "The stakes have never been higher for university applicants. With tuition fees set to treble from 2012, demand for places this summer is likely to be unprecedented.
"I fear that clearing will be the most frantic and stressful in living memory with thousands of young people, encouraged to aspire to university throughout their lives, left disappointed.
"Those who are unable to get a place this year face the prospect of having to pay the highest public university fees in the world. The Government's funding plans will leave students with mortgage-size debts and create huge instability within the sector.
"It's hardly surprising that English universities are bracing themselves for a drop in numbers in 2012, when they will also be contending with an 80% cut to their teaching budgets."
A spokesman for the Department for Business, Innovation and Skills (BIS) said: "Going to university is a competitive process and not all those who apply are accepted. We provided an additional 10,000 places last year and universities will again be able to recruit the same number of new students this autumn."
According to UCAS figures, as of July 18, 673,570 people had applied to university for this autumn, a 1.3% increase on 2010.
Of these applicants, 568,652 were from the UK.
Last year, around 47,000 people found places through clearing.