Tony Blair has said controversial school reforms are needed in England because the system is "not working well enough" for many children.
He told the Commons liaison committee that a "far greater diversity of supply" could raise standards.
The government has offered compromises over proposed "trust" schools in a bid to win over more than 90 Labour MPs who fear a "back door" return to selection.
Tories, who support reforms, accused Mr Blair of "giving in" to backbenchers.
But Mr Blair said the "heart" of the Education White Paper, published last autumn and seen as an important test of the government's authority, remained "in full".
The government proposes setting up independent "trust" schools, with more say over admissions and budgets, taking more powers away from local authorities.
Mr Blair said there was not currently a "single-tier system for all our kids" and that parents could not be expected to send children to failing schools to help "social engineering".
He added: "We do know what works.... you can see the schools that are the ones that are pushing ahead.
"They are the ones which, within proper rules in relation to selection and so on, develop their own independent sense of culture and ethos and are able to give a sense that a school is not simply part of a system but is a school that is special in itself."
Many Labour backbenchers fear the government's plans could mean a return to academic selection at age 11 and increase inequalities between working-class and middle-class pupils.
To head-off a rebellion, ministers offered a set of compromises on Monday.
The key points of the offer include:
- Strengthening the existing schools admissions code, but not writing it into law
- Banning schools from interviewing pupils and parents
- Allowing local councils to build new schools
- Increasing powers of admissions forums so they can object if they feel a school is not abiding by the admissions code
- Allowing the schools adjudicator to rule against creation of new trusts
Ministers have, however, rejected calls for schools to be set "benchmarks" for the number of children from poorer backgrounds they admit.
The Labour chairman of the Commons education select committee, Barry Sheerman, said parents would "know from now on that they've got a fair chance against any other" of getting their children into good schools.
However, ex-Labour education secretary Lady Morris, a critic of the white paper, still had some concerns and said she would be waiting to see what the text of the bill said when it is published later this month.
The Conservatives have supported the reforms in the white paper and urged Mr Blair not to give in to his rebel backbenchers.
Tory leader David Cameron said: "I think the education reforms are a step forward but I'm obviously disappointed that Tony Blair is spending his time giving in to his backbenchers... he doesn't have to cave in, because he's got Conservative support.
"If it turns out that the bill still reflects the white paper then obviously we will back it because we think the white paper is good for education."
Liberal Democrat education spokesman Ed Davey said: "Blair and Kelly can continue to spin but these compromises represent a real Government climb down.
"If the Government want Liberal Democrat support they will need to convince us these measures have real teeth."