Record numbers of A-level students are being turned away from the country's leading universities, it emerged today, as institutions declared themselves full more than a week before the clearing system, which allocates last-minute places, opens.

A Guardian poll of 38 universities reveals that increasing demand for degree courses – up 11.6% this year – intensified by the recession and a cut in available places means that nine days ahead of A-level results, even some of the brightest teenagers in the country, predicted to achieve more than 90% in their exams, are failing to secure a university place.

Birmingham, Bristol, Edinburgh and Warwick already have no places left on any of their courses. The London School of Economics and St Andrews said they would have to turn down students who narrowly missed the offers they received from other universities. Oxford and Cambridge, in line with previous years, will have no places left.

Last year almost 48,000 students found a university place through clearing – when institutions that have spare spaces match-make students who have not made their offers for other universities or apply late.

But the university admissions service Ucas said the number of places in clearing this year will be "even briefer and tighter than last year".

Admissions tutors predict that clearing places vanish within two to three days of A-level results. University leaders predict that as many as 170,000 students could find themselves left without a place on a degree course. Last year the figure was 130,000.

The intense competition for places has forced institutions such as Warwick, Cambridge and the London School of Economics (LSE) to turn down even students predicted to get an A*, the new grade introduced this year which was meant to enable universities to pick out the brightest students. Students need to achieve a mark of 90% or more to obtain the grade.

The LSE said pressure on places made it "inevitable" that pupils who were predicted at least one A* would be turned down. Warwick and Nottingham universities said it was even possible that a student with a clutch of A* predictions could still be turned down.

Cambridge has said it may have rejected up to 8,000 applicants expected to achieve at least one A*. The university is considering raising its minimum entry requirements from one to two A* grades in two or three years.

The Guardian's poll reveals that some universities will only offer students a place in clearing if they have three As. Manchester University said it would have 50 places in clearing, but those in humanities would need to be straight-A students.

Warwick said that to gain a place on a physics degree in clearing a teenager would need three A-grades, including in maths and physics, or an AAB with an A in maths and a B in further maths. Sheffield said students applying for degree courses in English would have to achieve two As and a B, while Leicester said that "where vacancies exist, we will be seeking two As and a B".

Nottingham will have under half the number of places in clearing it had last year – below 50. "Tough competition means we will be turning away some very highly qualified students with two As and a B rather than three As," a spokeswoman said.

Pat McFadden, Labour's shadow skills secretary, said this year's scramble for places had been made worse by the coalition government withdrawing 10,000 university places.

The Labour government planned to provide 20,000 places for this autumn but this number was halved when the new administration came into power. The universities minister, David Willetts, has said that sixth formers who fail to secure a university place should start a business or apply for an apprenticeship instead.

McFadden said cutting the number of university places reduced opportunities for people to improve their skills. "This is very shortsighted," he said.

Universities said the threat of fines for over-recruiting students had also made them cautious about taking on too many students. For the first time this year, 60 universities and further education colleges were penalised £15.67m for over-recruiting 4,235 students. The rise in applications has been attributed in part to the recession and a wider shortage of jobs for school-leavers.

The university thinktank Million+ has warned that the poorest students are the most likely to miss out. Pam Tatlow, chief executive of the thinktank, which represents modern universities, said under-represented groups, such as students from deprived neighbourhoods, would miss out because they tended to have lower grades.

A spokeswoman for the vice-chancellors' umbrella group Universities UK said increased pressure on places would lead to a "challenging time for everyone".

"It is anticipated that the clearing process for this summer will be briefer and tighter than in previous years. However, universities are very experienced in handling high numbers of applications and they have been preparing for this peak time for many months now along with Ucas."