Lotteries should decide which pupils get places at all comprehensives, including faith schools, according to a report which found that children from middle-class families were still dominating the best state secondaries.

Research from the Sutton Trust, a leading education charity, found that only 5 per cent of pupils at the top 200 state schools in England qualified for free school meals last year, the yardstick of family poverty.

This compares with a national average of 13.4 per cent and is virtually unchanged from the proportion five years ago, suggesting that the degree of classroom segregation between children from rich and poor backgrounds has not narrowed since 2003.

The research, seen by The Times, suggests that religious affiliation is one of the key causes of social selection at the top 200 comprehensives as more than half of them are faith schools, which control their own admissions.

The findings coincide with the launch this weekend of Accord, a powerful coalition of religious and secular organisations and commentators who say that state-funded faith schools should be barred from using religious belief as a criteria for admitting pupils or hiring staff.

James Turner, head of policy at the Sutton Trust, said: “We do not believe it is inevitable that those from low-income homes cannot succeed academically given the right opportunities, or that they should be less likely to access comprehensives with high academic standards, particularly when – as is often the case – these schools are on their doorsteps.”

It meant that nonprivileged youngsters were less likely to have access to the more rigorous academic pathways pursued by the best schools, that would then give them access to the country’s top universities.

The report recommends that oversubscribed schools adopt a lottery, or ballot, system as a more equitable way of allocating places than the present catchment area system, which allows well-off parents to buy their way into a good school by moving near by.

A handful of local authorities, including Brighton, experimented successfully with lotteries last year. Mr Turner said that lotteries would be particularly appropriate for faith schools to prevent them creaming off the most middle-class children.

“Instead of having tests to see who has the best letter from the priest, as long as children subscribe to the faith they could be entered into a ballot for places,” he said. He also advocated fair banding, whereby schools are required to admit equal proportions of pupils from each band of ability.

While the report’s findings on social class segregation will be of concern to politicians of all parties, few will be comfortable with its suggestion that faith schools adopt a ballot system.

David Laws, the Liberal Democrats’ schools spokesman, said that the pupil premium proposed by his party, which would give heads more money for educating children from deprived backgrounds, would also help by providing an incentive for schools to have a more balanced intake.

Michael Gove, the Shadow Schools Secretary, declined to comment.

Public opinion on faith schools is divided and politicians – no matter how committed to greater equality in state schools – are reluctant to take on the powerful faith school’s lobby.

The faith groups have seen off previous attempts at reform, most recently when the Government tried to force them to open up 25 per cent of their intake to children of other faiths or none. An ICM poll in 2005 found that 64 per cent of the public agreed that “the Government should not be funding faith schools of any kind”. But parents with children at England’s 6,000 faith schools, which account for a third of all schools, defend them passionately, pointing out that it was the churches who provided the first schools in England.

The supporters of Accord regard faith schools as “a self-serving club” for organised religion and argue that every school should welcome children from all backgrounds to promote social harmony. They also oppose laws coming into force on Monday that will strengthen faith schools’ right to specify the faith of head teachers and teaching assistants.

The coalition’s supporters include Philip Pullman, the author, A. C. Grayling, the philosopher, Adam Hart-Davis, the historian, Rabbi Dr Jonathan Romain, the Christian think-tank Ekklesia, the British Humanist Association and the ATL teaching union.

Last year the Government made it easier for faith schools to be created, but also encouraged all the major faith groups to sign a Faith in the System agreement that committed them for the first time to working together to promote community cohesion.

— One in 20 national curriculum test papers taken by 14-year-old pupils has still not been marked, Ed Balls, the Schools Secretary, has admitted.

Times recommends

• Students abandon the drink for gyms and juice
• Ofsted: third of Baby P-style reviews inadequate
• Top boys' school picks first woman head