Sixth-formers are facing the toughest competition yet for university entry because of an early increase in applications and a shortage of places for next year.

Documents seen by The Times show that most of the extra places pledged by the Government for 2010 have already been spoken for. A rise of at least 15 per cent in applications, compared with the same time last year, is expected to be announced by Ucas today, increasing the shortage of places.

The pressure on A-level students is likely to be more intense than this summer, when there was a rise of 10 per cent applying, a record level of interest and tens of thousands of capable candidates missing out. The deadline for submissions to the university admissions service for next year is not until January, but already leading institutions are reporting high rates of return on Ucas forms.

Schools are urging A-level students to apply early in the hope of snapping up places, and admissions tutors are warning prospective students to prepare themselves for disappointment.

Alistair Jarvis, from the 1994 Group of research-intensive universities, said that the best universities would not be able to take more students unless they were funded to do so. "Our institutions would like to meet the extra demand but they need government funding to do so. [Without it] they wouldn't be able to guarantee quality," he said.

The Government has promised 10,000 extra places for next year but only 2,396 of those are for new full-time undergraduates, official figures show. University leaders say that this is far below what is needed to cover the huge rise in numbers applying.

Priority for the 2,000 extra places will be given to "vulnerable subjects and healthcare courses", David Lammy, the Universities Minister, said in answer to a parliamentary question tabled by the Conservatives and seen by The Times.

The figures suggest that arts courses including English and history could be without additional numbers next academic year.

Pam Tatlow, chief executive of million+, which represents new universities, said that more needed to be done to help students who wanted to go to university. "[In previous years] early indications of increased demand have acted as a weathervane as to what the interest is in universities throughout the year," she said. Members had reported applications up on last year, she added.

Oxford and Cambridge, which have already closed their doors to prospective students for next year, are expected to publish large increases in numbers of applicants today. Last year the prestigious universities had 10 per cent more candidates than in 2007.

David Willetts, the Shadow Universities Secretary, said that those students finishing school next summer could face a crisis in the number of university places at least as severe as this year. "The extra demand in places was predictable but the Government failed to prepare for it," he said.

"We have outlined a plan for 10,000 fully funded extra places, which would go some way to ensuring that thousands of young people who want to go to university and get the necessary grades won't be left on the scrapheap."

At the same stage last autumn 64,500 students had applied to Ucas - a 6 per cent rise on 2007. By the end of the cycle in August this year, numbers were up 10 per cent to a record 609,000.

The recession-fuelled rise will be compounded this year by the numbers in the system who have already secured a place through deferred entry and those returning to Ucas having missed out on places in clearing in August.