Ministers should back down on English school reforms to prevent "back door" selection, Labour members of the Commons education select committee say.
The Education Bill is due in February
A report seen by the BBC says councils should get powers to set "benchmarks" to ensure balanced intakes at planned independent "trust" schools.
This demand has been explicitly rejected by the prime minister.
Tory members of the committee refuse to accept the report and have compiled their own, backing government plans.
Friday's final committee report - by the Labour MPs - will amount to a demand for government policy to be massively re-written.
The education committee split down party lines after efforts to reach concessions.
Tory members' "minority" report, seen by the BBC, calls on the government to stand by its original proposals.
The Tory MPs go further than the government in arguing that, in time, ministers should be able to "compel" all schools to become independent.
But Labour members of the committee are also challenging Mr Blair's position on several fronts.
They want trust schools to be denied total control of assets.
The proposed schools commissioner should be granted "strategic oversight" of the admissions process, they say, while looking at "wider social responsibilities on social segregation".
The success of the schools plan - set out in the Education White Paper - is seen as central to Tony Blair's authority.
Some 90 Labour backbenchers have signed up to an alternative version which calls for a national admissions code to be made statutory.
Tory leader David Cameron has said he will support the government's plans, as long as they are not diluted to placate Labour rebels.
But the prime minister is unlikely to want the resulting Education Bill to pass because of opposition support.
The Education Bill is due to be published in February with a vote expected in the Commons sometime in March.