Vivian Anthony, newly-retired after 10 years as secretary of the Headmasters' and Headmistresses' Conference of leading public schools, warned that "social engineering" would also drive talented students overseas and could challenge the position of Oxford and Cambridge universities.
Selection criteria must be "up front and known to all applicants", he told the HMC's annual meeting in Harrogate. "To select on the basis of postcodes or the poor overall performance of the candidate's school seems fraught with dangers.
"How long will it be before parents pursue university selectors in the courts for discrimination and abuse of human rights?" he asked, adding: "There will be no real fairness in the system until applications contain no mention of the candidate's school or background."
The former chief examiner and headmaster of Colfe's - a London independent day school - said it had become easier to achieve higher A-level grades.
"In the proper effort to widen access to A-levels and other post-16 courses, challenges to the most able pupils have taken second place," he added.
The way forward, he said, was for the brightest sixth-formers to work at the level of first-year undergraduates, perhaps in partnerships between schools and higher education institutions.
He also called for exam boards to rethink the way A-level results were presented so that top niversities could distinguish between "candidates of real distinction and those who have just scraped an A or B and who 10 years ago would have scored two grades lower".
Mr Anthony warned that new, modular A-levels would mean at least 50 per cent more time in exams, producing serious timetable implications in summer 2002.
The public school heads met secure in the knowledge that New Labour had learnt to like them and would never try to remove parents' right to choose them for their children.
Estelle Morris, the school standards minister, gave these assurances in a frank interview in Conference and Common Room, the journal of the HMC.
Speaking to Anthony Seldon, the political biographer and head of Brighton College, she said there had been "a huge cultural change" since the days when Labour sought to abolish independent schools.
But she also revealed uncertainty within the Government about how the current partnership between state and independent schools should develop after the next election.
"Crime and punishment should be included in basic classroom teaching to combat 'startling' ignorance of the criminal justice system," David Calvert-Smith, director of public prosecutions, told the conference on Tuesday. His views were endorsed by the chief inspector of prisons, Sir David Ramsbotham, who suggested that schools encourage sixth-formers to become "peer role models" to young offenders.
Overseas exodus, 24 The Laura Spence affair should not tempt universities into social engineering, top public school heads heard this week.