The government has denied caving in to pressure after scrapping proposals to make new faith schools in England take children from other religions.
Under the plans, they would have had to reserve up to 25% of places for pupils from outside their faith.
But Education Secretary Alan Johnson said he had now reached a "voluntary agreement" with churches on quotas making legislation unnecessary.
Tory Lord Baker branded it the "fastest U-turn in British political history".
The Church of England and the Catholic Church have agreed to "ensure" that up to 25% of places would be reserved from children other faiths or no faith, Mr Johnson said.
In a letter, he said: "As we now have the support of the two major faith organisations in the country for our proposed way forward, I do not feel the legislative route is necessary or appropriate and no longer propose to lay an amendment to the Education and Inspection Bill."
But Lord Baker said he had dropped his own amendment on faith school places after ministers had promised to insert a similar one.
Speaking on BBC Radio 4's Today programme, he accused Catholic leaders of using "deception" in a campaign against introducing quotas, by hinting that the plans would be extended to all existing faith schools, not just new ones.
He said the government "must impose some means of integration" when funding schools.
Any requirement to provide non-faith places, where local circumstances make it appropriate and subject to public consultation, would be in addition to the demand for faith places
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Otherwise there was a danger of creating educational "ghettos", particularly in more than 120 private Muslim schools which he said aspired to enter the state sector.
Leaders of the Catholic Church and the Church of England welcomed the government's decision to drop its proposals.
Vincent Nichols, the Catholic Archbishop of Birmingham, said Mr Johnson understood it was "quite unacceptable to force into a new Catholic school 25% of people who were not particularly sympathetic to that faith".
The bishop, who chairs the Catholic Education Service in England and Wales, said future schools could now be planned "fully for the Catholic need" and further places could be added "according to local need".
But Lord Baker said only two new Catholic schools had been created in the last decade, compared with eight Muslim ones.
The latter had not always been inclusive, he added.
However, Mr Johnson said some Muslim schools had indicated they wanted between 20% and 25% of places to be for children from outside the faith - but very few parents wanted to take them up.
Although the voluntary agreement does not affect Muslim schools, the Muslim Council of Britain welcomed it.
ENGLAND'S FAITH SCHOOLS
Church of England 4,646
Roman Catholic 2,041
Education spokesman Tahir Allam said the compromise was "a good position to be in".
Half of all adults would be unhappy to send their children to a faith school where they were outnumbered by those from another religion, a poll for BBC Two's The Daily Politics suggests.
But 46% of the 1,009 people interviewed by Populus said they would be happy with this arrangement.
Under the government's previous plans, councils could have told new faith schools to take up to 25% of pupils from other religions, or no religion.
Parents and other groups could have appealed to the education secretary where they felt the quota imposed was unfair.
Shadow schools minister Nick Gibb welcomed the government's change of policy, saying it was "for schools themselves to decide".
Liberal Democrat education spokeswoman Sarah Teather labelled the affair a "dog's dinner".
The National Secular Society argued that the latest development would not make any difference, saying that it was up to the government to promote community cohesion.