Sussex University is full and will not be taking any students through clearing.
The university said that it had been so popular this year that it had not accepted any new applications for some courses after the first key deadline in January.
Overall, undergraduate applications to Sussex were up 20 per cent this year as prospective students aimed to beat the rise in tuition fees which takes effect this time next year.
The university, based in Falmer, said that the national average increase in applications was 5 per cent.
Professor Clare Mackie, the pro-vice-chancellor (teaching and learning), said: “This shows the effect of the attention to the student experience – and our consequent high standing in the national league tables – combined with the development of new programmes.”
Rob Evans, head of admissions, said: “This year our scope to be flexible with applicants who have missed their grades, even narrowly, is very small.
“For some well-qualified applicants who have missed their grades in over-subscribed subjects, but who have achieved A level grades equivalent to AAB, we are offering a deferred place for next year.”
This is possible because the government has allowed universities to admit, from 2012, an unlimited number of British and other EU students with grades of AAB or higher.
Current government funding rules limit the number of British and other EU students that universities can take.
Sussex is, however, still able to consider suitably qualified overseas students in most subjects.
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