The chairman of the Sutton Trust said most bursaries and scholarships were not means-tested and went to families who could afford places or children of staff.

Sir Peter said: “There is a lot of PR put out by private schools that they are funding children from poor backgrounds, but the reality is that very little support goes to underprivileged families.”

His comments follow the graduation of the first set of GCSE pupils at the UK’s only “open access” private school. Since 1999 Belvedere girls’ school, Liverpool, has accepted pupils on academic merit, regardless of parental ability to pay the pound;6,930-a-year fees.

The Sutton Trust, which contributes more than pound;2 million a year to fee subsidies at the school, hoped the approach would have been replicated elsewhere but, five years on, Belvedere remains the only one of its kind.

This week Sir Peter hailed the school’s record results, which saw 63 per cent of passes graded A* or A, but attacked the Government’s refusal to back the scheme further. “We have shown that a school like Belvedere can be a great vehicle for social mobility but there is a vested interest in maintaining the current system, where only those who can afford it get the best education,” he said.

The consultants haysmacintyre said in a report in March that 8.2 per cent of private school income was spent on fee concessions in 2002-03. This enables almost a third of private school pupils to gain a discount.

Professor Alan Smithers, from Buckingham university, who evaluated the Belvedere scheme, said its pupils had achieved better grades at 16 than had been predicted on entry.

A spokesman for the Independent Schools Council said money for scholarships had been limited since Labour abolished the assisted places scheme. He said it was not schools’ responsibility to channel the little money available to poor families. “Most schools regard themselves as academic elites, not agents of social engineering. They are keen to attract the best students, regardless of family background,” he said.