The 36 per cent rise is the first real indication that the predicted dash for the last free university places has begun to materialise, despite the Government's 11th hour U-turn over fees for gap-year students last week.
Some 12,700 people had made late applications via the clearing system, up from 9,300 at the same time last year.
Officials at the Universities and Colleges Admissions Service are still taking between 7,000 and 8,000 calls a day. About 80,000 people have also used the UCAS Internet service in its first year.
Many students were still asking about the question of fees for gap-year students, said UCAS deputy chief executive Anthony McClaren.
"In the light of the so-called U-turn," he said, "we are still getting enquiries from people who do not quite fit into the exemption the Department for Education and Employment has set up.
"The process of clearing itself is going very well and universities are processing applications more quickly than ever before."
A total of 249,576 students had been placed on courses as The TES went to press.
The National Union of Students, meanwhile, pledged to keep up pressure on the Government to give further concessions to students caught in the so-called gap trap.
A spokeswoman warned that many students had been advised to delay their applications until next year - leaving them facing the prospect of paying tuition fees when they are introduced for the first time.
Concern was also focusing on the 15,000 students studying for access courses, traditionally a route into university for people with few qualifications. Colleges have already warned that recruitment to access courses could be hit as people realise the cost of entering university in October 1998.
An NUS spokeswoman said people joined these courses intending to go to university, and so should also have their fees waived. Union officials are also angry about the position of those on pre-university foundation courses in subjects such as art.
Scramble for places, page 6