They have overcome the hurdle of the new A* grade and succeeded in the face of what has been described as the most intense scramble yet for university places.

But as the media interest around A-level results dies down, and despite the perennial claims of grade inflation, there is evidence that this year's students have proved themselves able to raise their game.

Richard Cairns, headmaster of fee-paying Brighton College, said the introduction of the A* grade had raised the bar, motivating his brightest students to work harder.

His school has compared the results of its students with A* offers from the University of Cambridge and Imperial College London with those of students who had non-A* offers from comparable institutions, including the University of Oxford.

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"Students who had an A* offer worked much harder and ended up with three A*s on average, whereas those without an A* offer averaged one-and-a-half A*s," he said.

Across the UK, a total of 8.1 per cent - or one in 12 - of A-level entries were awarded the new A* grade last week, while per cent of papers achieved an A or A*.

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The proportion of the new top grade was highest in independent schools, where 17.9 per cent of entries received an A* grade, compared with 5.8 per cent in state schools.

Students with offers from Cambridge received an impressive average of 2.5 A*s each.

Of these, 57 per cent (3,959) were achieved by students attending state schools, 40 per cent (2,817) by students at independent schools and the remaining 3 per cent (197) by those at other institutions, mostly overseas, according to Geoff Parks, head of admissions at Cambridge.

While the average number of A*s achieved by Cambridge applicants from independent schools was "slightly higher" than among those from state schools, Dr Parks said his preliminary analysis suggested that the difference was accounted for by the former group being more likely to take further maths at A level, the subject with the highest A* rate.

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"It would indeed appear that the opportunity to gain an A* grade has encouraged students to keep their foot on the gas in Year 13," he said.

A spokeswoman for the University of Oxford said it did not have comparable data, but that more than 90 per cent of students with Oxford offers achieved at least one A*.

rebecca.attwood@tsleducation.com.