Geoff Parks, the director of admissions, said that 5,325 unsuccessful applicants went on to get three A grades last summer. Cambridge admitted 3,293 undergraduates in October, 93 per cent of whom had three A grades.

Dr Parks urged Ruth Kelly, the Education Secretary, to accept proposals for a new diploma to replace A levels, GCSEs and vocational qualifications.

Ms Kelly is due to publish the Government’s long-awaited response tomorrow to the plan for a diploma set out by Sir Mike Tomlinson, the former head of Ofsted.

But she has already declared that A levels will stay amid Government concern that abolishing the “gold standard” qualification would alienate middle-class parents on the eve of a general election.

Dr Parks said that Cambridge was strongly in favour of the Tomlinson proposals, which would help to distinguish the most able students from the overwhelming numbers now achieving maximum grades at A level.

“It is very hard for a lot of the kids because there is no tangible reason why they have been turned down in favour of somebody else with the identical exam record. It boils down to our judgment at the margins,” he said.

He did not understand the Government’s desire “to hold on to the terminology” of A levels. Dr Parks said: “I have had so many conversations with people who would be regarded as middle class who ask me whether their kids should be doing the International Baccalaureate because the A level is so discredited.

“I don’t think it is discredited in everybody’s mind but what happens with the results every August shows that there is some concern that it does not do at the upper reaches what it used to do.”

Exam papers now contained fewer open-ended questions that allowed students to demonstrate knowledge and originality of thought. Instead, there were more questions that “students could be lead through” because this made it easier for exam boards to ensure consistency of marking.

“It makes for more reliable assessment but it does mean that the opportunity to demonstrate your real ability is lost,” Dr Parks said.

Sir Mike proposed new ways to stretch able students as part of the diploma, including extra questions that would lead to A-plus and A-plus-plus grades for the top five per cent of candidates. Ms Kelly is reported to be planning a new vocational diploma to stand alongside A levels as part of the Government’s response. Dr Parks said that this would fail to achieve the “parity of esteem” between academic and vocational courses that ministers desired.

“If when you open up a prospectus and the criteria for entry are all listed in terms of A levels, then it sends a clear message about what we are looking for,” he said.

“If there is going to be parity of esteem for different sorts of qualifications there is no way that is going to happen if you have a terminology that reflects back to a system where A levels mean something in particular. Changing the names would signal that you have a new system that works differently.”

Cambridge’s admissions statistics showed that 14,684 people applied for places last year compared with 13,700 in 2003, an increase of 7.2 per cent. The number accepted went down by 142 to 3,293 because the university had admitted more students than expected in 2003.

The increase in applications was matched by the rise in the proportion of rejected candidates with three A grades. It went up by 7.2 per cent from 4,966 in 2003 to 5,325 last year.

The proportion of women admitted last year rose by three percentage points from 49 to 52 per cent. Entrants from state schools increased by one percentage point to 56 per cent of the cohort.

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