Downing Street has hinted the government might be ready to compromise with rebel Labour MPs to get school reforms for England through Parliament.
Fair access to schools must come first, say the MPs
More than 90 MPs have raised concerns the Education White Paper might see a back door return to academic selection.
But a Commons education select committee report is calling for more safeguards to prevent this.
Tony Blair's spokesman welcomed the report as a "serious piece of work" that ministers might "refine".
The government's Education White Paper, published last year, is seen as central to the prime minister's third term in office.
It proposes setting up independent "trust" schools, with more say over admissions.
More than 90 Labour backbenchers have signed up to an alternative white paper, which calls for the existing national schools admissions code to be made statutory.
But the government says the code is too complex to be included in the forthcoming Education Bill and already offers enough of a safeguard against a return to academic selection.
The committee agrees with ministers that the code should not be made statutory, but is calling for extra protective measures.
- Local authorities and schools commissioner to have a "new vigorous role" monitoring admissions
- A complete ban on interviewing and selecting some pupils by "aptitude"
- "Benchmarks" for how many children schools take from poor backgrounds
- Fair access to come ahead of diversity and choice
- Local authorities to report every year on admissions arrangements in their areas
These measures may be seen as the basis for a compromise between ministers and Labour rebels.
The prime minister's spokesman said the government was "going to study the report and make suggestions as to some things that might be refined."
BBC political correspondent Carolyn Quinn predicted "a lot of brinkmanship" between ministers and rebels.
She added: "Nobody will blink first but there might be a compromise by the government to buy off enough of the rebels."
In its report, the committee warns: "There is a danger that a poorly managed choice agenda could accelerate the flight from schools in deprived areas.
"This would further disadvantage those who are already disadvantaged in education."
The committee's chairman, Labour MP Barry Sheerman, told BBC Radio 4's Today programme that "delivering good education" for all meant paying attention to the "social mix that goes into schools".
The report urges the government to look at choosing pupils on an anonymous basis, so parents adept at working the system cannot get an unfair advantage.
It also says schools have a "lack of enthusiasm" for trust status.
Lib Dem education spokesman Ed Davey said the report was a "major blow" to the government, which would have to look for compromise.
Conservative MPs on the education committee are at odds with their Labour colleagues and have published a "minority report", urging the government to "keep to the word" of the white paper.
Tory leader David Cameron is backing trust schools.
Tony Blair has admitted he is performing a "high-wire act" on the schools issue and is thought to want to avoid relying on Conservative support for the measures to get through Parliament.
Education Secretary Ruth Kelly has given a "categorical assurance that there will be no new selection by ability."
Ministers are due to publish the full Education Bill in Parliament next month, with a vote in March.