Tony Blair and Ruth Kelly came out fighting to defend the Government's plans for school reform today after offering a string of concessions to Labour rebels.

In a move that prompted criticism that he was becoming a lame duck, the Prime Minister authorised a series of compromises yesterday to quell the rebellion of up to 96 Labour MPs who opposed his controversial plans to make schools more independent.

But today, Mr Blair told MPs that the core of the reforms remained intact.

"The freedoms that will remain are precisely the freedoms set out in the White Paper: schools will have the freedom, as of right, to become self-governing trusts; they will be able to own their own assets, manage their own staff, develop their own independent sense of freedom and culture," he told the House of Commons Liaison Committee.

"That is the heart of reform and that remains in full," said Mr Blair. "We are not going to achieve the step change I want in education unless we are prepared to be fully supportive of those things."

Last night, the Education Secretary, Ms Kelly, offered Labour backbenchers extra measures to end academic selection by the back door. She also gave an unexpected reprieve to community comprehensives, meeting two key demands of the rebels.

Although many Labour MPs appeared ready to back the compromise, Mr Blair's flagship education plans still hang in the balance because some left wingers still oppose them - and because the Conservatives, who have so far backed the Prime Minister, said that the climbdown may force them to reconsider their support.

If the Tories withdraw their support, the Bill could still be lost. The first vote will be early next month.

Earlier Ms Kelly said the compromise left the "key ingredients and key building blocks" of the reforms in place. Insisting that the party had always supported the "overwhelming majority" of the Bill, she said last night's compromise was a response to a handful of specific objections from backbenchers.

"They weren't looking for the building blocks of the White Paper to be torn out," she told BBC Radio 4's Today programme. "They were looking for additional safeguards on a couple of particular points."

The concessions mean all interviews, even at religious schools such as the London Oratory chosen by Mr Blair for his sons, will be explicitly banned in the new schools Bill, a particular grievance for many rebels. The admissions code, which prohibits academic selection, will be given legal force with all schools obliged to act "in accordance" rather than "have regard" to its terms.

Local admissions forums, made up of councillors and school representatives, will be given new powers to crack down on schools they suspect of selecting.

After weeks of agonising, Mr Blair also threw a lifeline to community schools by allowing local authorities to build new comprehensives. This had been ruled out by the Schools White Paper published last year, to the horror of many Labour backbenchers.

However, to protect the principles underlying Mr Blair’s plans for new self-governing trusts, the Bill will make clear that local authorities cannot be commissioners and providers of new schools.

An authority seeking to build a new comprehensive will require the approval of the Education Secretary before it enters a contest with a proposed trust. Up to 100 new schools are built every year.

Questioned about the concessions today, Mr Blair defended the decision to stop schools selecting by interview. Despite repeated allusions to the London Oratory, which recently won a court case to continue interviewing the parents of prospective pupils, the Prime Minister refused to comment on a individual school.

"It would be absurd to say that is the difference between a good school and a bad school," he said, on the subject of interviews. "There are, I think, only a handful of schools in the country that do interviews as a method of selection and the churches have already indicated that that is bad practice."

The Conservatives have left open the prospect of backing the Bill, but attacked the Prime Minister for bowing too readily to backbench pressure.

"I think the education reforms are a step forward but I am disappointed that Tony Blair is spending his time giving in to his back benchers," David Cameron, the Tory leader, said today. "He doesn’t have to back down or cave in because he still has Conservative support."

"If it turns out that the Bill still reflects the White Paper then we will back him. Giving schools greater independence will lead to higher standards and more diversity in this country."

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