A study by the left-leaning Institute for Public Policy Research has found that intakes at non-faith schools such as academies, who act as their own admissions authorities, were six times more likely to be "highly unrepresentative" of the ability and social class of local pupils than community schools.
Faith schools with their own admissions policies were 10 times more likely to be unrepresentative.
The report urges the Government not to extend the number of academies and trusts without making the system fairer.
Its authors claim that some schools are still able to select pupils covertly, by confusing applicants with intimidating admissions literature, for example.
They recommend that if the new admissions code proves ineffectual, academies, trusts, foundation and faith schools should be drawn into a local system with an independent admissions administrator.
Richard Brooks, IPPR head of public services, said recent reforms to prevent schools selecting were welcome, "But the system is like asking pupils to mark their own essays while providing them with detailed rules designed to prevent them from cheating."
The think tank warnings come less than a week after the Conservatives said that schools in inner-city areas should be allowed to select pupils according to race, to create a more even racial balance in classrooms.
David Willetts, the shadow education secretary, made the proposals in reaction to new figures showing the extent of racial segregation in some English towns.
In Blackburn, four out of nine secondary schools attract more than 90 per cent of their pupils from one ethnic community.
But Chris Keates, general secretary of the NASUWT teachers' union, said:
"It's dangerous to start talking about selecting pupils on the basis of race.
"It's a well-meaning, but ill-conceived idea. What we need is fair and transparent admissions arrangements."
Her concerns were shared by Baljeet Ghale, president of the National Union of Teachers. "The idea of shipping in pupils or even teachers as exhibits, to achieve an ethnic balance is not really the answer to the problem," she said.
The think tank report also recommends that oversubscribed schools should select by "fair banding" to generate more representative, mixed-ability schools.
In the long term, it says, fair-banding should be applied across schools in whole areas. Faith schools could also select by ability banding, but could give priority to applicants on the basis of faith within each band.
* Find 'School Admissions: Fairer Choice for Parents and Pupils' at www.ippr.org.uk