Sir Peter Lampl spoke out as the education charity he chairs, the Sutton Trust, published evidence which shows that the country's top-performing comprehensives are socially exclusive and are not taking their fair share of disadvantaged pupils.
The research also revealed that schools that governed their own admissions - which the white paper proposes creating more of through trust schools - were disproportionately represented in the top 200 and were the worst at admitting a representative share of pupils in their area who are entitled to free school meals.
Sir Peter wants to see a ban on faith schools basing their admissions on religion, and benchmarks set by local authorities for the number of disadvantaged pupils that each school should admit.
"We have got a socially selective system in this country that we cannot just let drift on," he said. "This isn't something that is going to happen when we introduce trust schools. It is already there."
His comments came as an Institute for Public Policy Research report expressed concern about trust schools. It said evidence showed that there is a clear relationship between schools controlling their own admissions and potential selection and that admissions need to be rigorously policed at a local level.
The report drew on a study of admissions systems in the United States which found that the socio-economic mix of pupils in a school had an impact on attainment and was more likely to affect middle-class pupils than those from lower social classes.
The Sutton Trust study found that the proportion of pupils eligible for free school meals in the top 200 comprehensives was 5.6 per cent, compared with the 11.5 per cent in their postcode areas and the 14.3 per cent average for state secondaries in England.
Comprehensive schools controlling their own admissions accounted for 139 (69 per cent) of the top comprehensives, but only 31 per cent of state secondaries.
These schools were socially unrepresentative of their neighbourhoods, with 5.8 per cent of pupils eligible for free school meals, compared with 13.7 per cent in their local areas.
The remaining 61 top comprehensives, whose admissions were controlled by the local authority, were generally found in affluent areas with average free-meal rates of 5.9 per cent, well below the national average. "It is clear the current system is not working equitably," Sir Peter said.
Schools should control their own admissions, but only within a more robust code enforced by local authorities.
The onus should be put on schools that did not take proportionate numbers of disadvantaged pupils to do something about it.
The report also showed that 42 per cent of the top comprehensives were religious schools which had an average of 15.2 per cent free school meals in their areas but only admitted 5.9 per cent.
Sir Peter said: "If you sign for the programme for your child and are prepared to have that faith taught by the school, whether you are part of that faith or not should not be a deterrent."