University admissions service UCAS said 135,114 students were already eligible for clearing this year, but it is thought that only 22,000 places are available.
At this time last year about 109,000 people were eligible for clearing and double the amount of places (44,000) were available.
This year's record A-level results have put added pressure on the admissions system, which is facing a shortage in places caused by a surge in applications.
Most of the UK's leading universities have already said they are full, while others say they have few places left available, leaving up to six students chasing every spot.
Ucas today confirmed that record numbers of students have had their university places confirmed (371,016 applicants), but almost two fifths were still waiting to hear if they had been successful.
Some 135,114 would-be students have qualified for clearing because they have either not met the grades required by their course, have chosen not to take up an existing offer, or were not holding an offer.
Clearing is the annual process of matching applicants to vacant university courses.
Ucas, based in Cheltenham, Gloucestershire, said there were 609,155 university or college applicants in total this year, up some 10% on last year.
Some 96,806 applicants were still awaiting a decision on places today, up 15% on last year.
Withdrawn applicants amount to 6,219, a figure roughly equal to last year.
It has been estimated that up to 50,000 applicants could miss out on a place this year, but universities minister David Lammy said today that both he and Ucas did not recognise the figure.
He told BBC Radio 4's Today programme: "You simply can't deduce that kind of number at this stage."
Every year, one in five young people who applied to university did not go for various reasons, he added.
Speaking at the Ucas centre today Mr Lammy stressed that thousands of courses were still available.
He said: "We will do all we can to support Britain's young people, to back them at this time. Young people who are not successful may wish to go back for re-takes and we are supporting the sixth form colleges in bigger numbers than ever."
The number of courses showing vacancies for EU and UK students is 31,163. But that is not the same as the true number of available clearing places for individuals, which is expected to be lower, UCAS said.
The figure shows several different choices of course relating to the same subject, where there may be only one place available.
For example there might be several different types of nursing course offered - to give options - but once one of them is taken up, the others are withdrawn.
There are a further 8,326 courses showing vacancies for non-EU students, as there is no cap on their places because they pay full fees.
Kate Butland, UCAS customer services manager, said her staff would be taking some 15,000 calls today alone from anxious students and parents.
Her 110 staff would be consoling and encouraging in equal measure, but above all telling callers not to panic despite the reported scramble for places.
Ms Butland said: "Calls are taking slightly longer this year, partly because of the reduction in places, and because of the adjustment period (dubbed trading-up) where those who exceed expectations can now speak to institutions they wouldn't normally do."
A message on UCAS's Twitter thread today apologised for busy phone lines, promising to answer calls as soon as possible.
Diana Warwick, chief executive of vice-chancellors' group Universities UK, said: "Universities are experienced in handling high numbers of applications and they have been preparing for this peak time for many months now, along with UCAS. There will be a range of UCAS and university advisers available to help those applicants who have not gained a place initially."
Dr Wendy Piatt, director general of the Russell Group of leading universities, said: "Competition for places at Russell Group universities has always been tough. This is because students see their degrees as intellectually challenging as well as the basis for getting top jobs after graduating.
Liberal Democrat universities spokesman Stephen Williams said: "The irony is that while a record number of students have achieved the top grades, more young people than ever are going to be disappointed as they fail to get a place at university.
"Ministers must accept the blame for making this situation far worse by failing to fund the number of extra places they originally promised."
Wes Streeting, president of the National Union of Students (NUS), said: "We remain concerned that, despite passing their A-levels today, many university applicants will still be disappointed.
"The Government may have recently increased university places by 10,000, but thousands of people who have applied to study non-STEM subjects are going to be without a place this summer."
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