Martin Hammond, head of Tonbridge School, Kent, said his boys no longer applied to one of the university's best-known colleges, King's, because it was biased in favour of state schools.
With the exception of music scholarships, he said, he was advising his pupils against applying to King's - founded in 1441 and noted for its choir and Christmas services of carols and lessons - because it was "too left-wing" and followed a "policy of social engineering".
Vivian Anthony, secretary of the Headmasters' and Headmistresses' Conference of independent school heads, said that the issue appeared "almost every year" on the agenda for meetings the conference has with the university.
"Somebody raises the issue of bias and somebody else (from the university) says, 'Nonsense, there is no bias, we are just trying to make special arrangements for particular individuals who would otherwise have little chance of getting in'." But there did appear to be "some engineering" which independent schools found frustrating when good students did not get a place.
"People get very wound up about it," Mr Anthony went on. "My members believe that from time to time their good people haven't been treated 100 per cent fairly. The colleges' job should be to find the best people. We would regard it as unfair if a person was turned down in favour of somebody less good simply because they came from a less advantaged background."
Seventy per cent of students at King's are from state schools compared with a typical 50-50 split with the independent sector across the whole university. Yet an independent pupil still stands a better chance of getting into King's than a state student.
Perhaps because of its egalitarian reputation, it attracts 80 per cent of its applications from the maintained sector, but independent schools gain 30 per cent of the places with only 20 per cent of the applications.
Ceri Smith, Cambridge University Students' Union academic affairs officer, said: "I'm from a public school and we were told, 'Don't apply to King's whatever you do, because they're all lefty scum.' The public schools are paranoid."Reuse content