The Institute for Public Policy Research (IPPR) announced next month's release of its Fair choice - choosing a better admissions system report as local authorities in England prepare to write to parents this week with offers of secondary school places for this autumn.
Other schools under fire from the IPPR over independent admissions policies were academies, foundation schools and trust schools.
According to the IPPR report, every school should be part of a local system of admissions "order to give parents a fairer choice of school places and to help tackle educational segregation".
IPPR welcomed the Admissions Code reforms but said that unless it results in "significant reductions" in segregation by income and ability, schools should "cease to be their own admissions authorities and local education authorities should take over this role instead".
New research from the IPPR claims that faith schools which are their own admissions authorities are ten times more likely to be "highly unrepresentative" of their surrounding area than faith schools where the LEA is the admissions authority.
The think tank said, meanwhile, that non-religious schools with their own admissions policies are six times more likely to be "highly unrepresentative" of their surrounding area than community schools - for whom the local education authority is the admissions authority.
In light of its findings, the IPPR is recommending that the no school administer its own admissions process but that there should instead be an independent admissions administrator in every local education authority.
The IPPR report also recommends that faith schools should adhere to 'fair banding by ability', although it said that faith schools could give priority to applicants on the basis of faith within each ability band.
The report will call on Local Admissions Forums to produce a regular report on levels of segregation by income and ability in their local schools.
"We need a system of fair choice for all parents and pupils. At the moment, schools that control their own admission arrangements are selecting their pupils, and our classrooms are more socially segregated than the local communities outside the school gates," said Nick Pearce, IPPR Director.
He said the reforms to the Admissions Code were welcome but said the new system is "like asking pupils to mark their own essays, while providing them with detailed rules designed to prevent them from cheating".
"Schools can run themselves and develop a strong individual ethos without needing to operate their own admissions policies," he said.
Adrian Pritchard, Head of School Development at the Church of England said, "Until we've seen the piece of research properly it is very difficult to comment on it but certainly the figures they (IPPR) used do not reflect any of the figures we possess."
Last week, leader of the Conservatives David Cameron revealed his intentions to send his three-year-old daughter Nancy to a faith school. He is believed to be enrolling her in a Church of England primary school two miles away from his west London home.
In defence of his plans, Mr Cameron insisted that a smaller state-funded church school would offer more "familiarity", saying he supported faith schools and made no apologies for identifying one for his daughter.
"I'm quite a fan of faith schools and we're looking at a church school we're very keen on," Mr Cameron told BBC Radio 4's You and Yours programme, adding that he was a member of the "relevant faith".
Lord Adonis, the schools minister, last night rejected the IPPR's recommendations.
"We agree that ability banding can be an effective way of widening access, but schools should have the power and freedom to set their own admissions policies according to local needs," he said in a Telegraph report.
"The report is wrong to suggest that schools operate in a vacuum - by law they must consult widely on their proposed admission arrangements, with any objections being ruled on by the independent schools adjudicator."