Students from affluent families must pay the full cost of higher education tuition, Bristol University's vice-chancellor Sir John Kingman said this week.
Universities should compete for students, some of whom would receive means-tested government scholarships, according to Sir John, who delivered the university's annual Bolland lecture.
Sir John said: "The difference in public funding for a student from the very poorest family and one from the very richest is a mere £1,050 a year. The result is that public support of the universities is a social benefit taken up by those who need it least.
"The vicious circle can only be broken if the government targets its money at those students who need it most - and if better-off families pay the real cost of their children's education."
Teaching income would come from market-rate student fees meaning that the publicly funded block teaching grant could be abolished. Scholarships would be funded by government and institutions would be free to award their own scholarships.
"The universities would be in real competition, on quality and cost groundsI Universities would have a much stronger incentive to give value for money," he said.
Sir John is the second vice-chancellor from the Russell Group of research-led universities to call for top-up fees.
Sir Colin Campbell, vice-chancellor of the University of Nottingham, has championed differential fees since last year. Others have acknowledged the need for reform - Sir Richard Sykes, rector of Imperial College, London, has described flat-rate tuition fees as "not viable in the long term".
Differential fees have been backed by new Labour think-tank, the Institute for Public Policy Research.