Research conducted by the Headmasters’ and Headmistresses’ Conference and the Girls’ Schools Association will conclude that Oxbridge runs a fair and rigorous selection process.

The study - to be released at the end of the month - was based on examination of this summer’s admissions.

The report was commissioned amid fears that government pressure to widen access is squeezing privately-educated pupils out of the most prestigious universities.

Oxford and Cambridge have borne the brunt of this pressure - which has included a direct attack on their “establishment” bias from Chancellor of the Exchequer Gordon Brown - and have spent millions in the hunt for inner-city students.

But according to the two largest groups representing independent schools, Oxbridge remains impartial.

“Our impression is that they’re doing a good, professional, rigorous job in difficult circumstances including heavy pressure from government,” said Geoff Lucas, HMC secretary.

His view is backed by Sheila Cooper, general secretary of the GSA. “We haven’t got any major problems with these two universities,” she confirmed.

Although neither would pre-empt the results of the full survey, to be published on September 30, it is anticipated that some well-established institutions will come in for criticism.

Ms Cooper said that the findings would be used to advise members on what sort of response they are likely to get from individual universities. They are so concerned at the overall state of admissions, the exercise may well be repeated as an annual bias-watch.

In one sense it is no surprise that private schools should leap to the defence of Oxford and Cambridge as the two universities still take nearly half their successful candidates from the independent sector.

But the proportion is steadily declining - this year Cambridge estimates it will be down from 46 to 42 per cent - and some private school heads and governors are convinced that good students are now losing out.

Geoff Lucas, Platform, 23

The Issue, Friday magazine