Tony Blair bowed to his Cabinet and party last night by accepting that there would be no exemption from antidiscrimination laws for Roman Catholic adoption agencies.

In an attempt to soften the blow, the agencies will be given 20 months to prepare for the new laws. Until then there will be a “statutory duty” for religious agencies to refer gay couples to other organisations.

There will be a regular assessment by adoption and child welfare experts on the impact of the regulations to ensure that the existing expertise is not lost.

Mr Blair announced the deal last night after a weekend of talks with Cabinet colleagues and adoption agencies. The regulations will come before Parliament in a “take-it-or-leave-it” vote next month. MPs who feel that the transition time is insufficient will be able to vote only against the plans.

Mr Blair said he believed that ministers had found a “way through” to prevent discrimination and to protect the interests of children, which all “reasonable people” should be able to accept.

Ann Widdecombe, the former Shadow Home Secretary, said that it was not a compromise and meant that Catholic agencies would close.

The Conservatives will be given a free vote, with David Cameron voting for the regulations and David Davis, the Shadow Home Secretary, and several other frontbenchers likely to vote against. Labour MPs will be expected to vote for the proposals.

The preparation period is a compromise between Ruth Kelly, who was holding out for three years, as the Catholic Church wanted, and the time-span of as little as six months that was sought by several other Cabinet ministers, such as Alan Johnson, the Education Secretary. Ms Kelly, the Communities Secretary, who had proposed that Catholic adoption agencies should be exempted from the regulations, welcomed the deal.

She said: “The approach on adoption is a positive breakthrough in eliminating discrimination while recognising the need for a practical approach that ensures the most vulnerable children are found loving homes. This approach should be welcomed by everyone on what has been an extremely complex issue.”

Mr Johnson, the minister responsible for adoption, who refused to countenance exemptions when he was in charge of the equality regulations, said that detailed research by the Department for Education and Skills had indicated that any transition could be handled within six months.

But he welcomed the outcome nonetheless. He said: “This is the right outcome for all concerned because it puts the interests of children first.”

Mr Blair said: “There is no place in our society for discrimination. That’s why I support the right of gay couples to apply to adopt like any other couple. And that way there can be no exemptions for faith-based adoption agencies offering public-funded services from regulations that prevent discrimination.”

Ben Summerskill, chief executive of Stonewall, the gay rights group, accepted the proposed compromise. “We felt six or twelve months would be a reasonable period for agencies to retrain their staff but if it takes eighteen months to reverse a thousand years of prejudice, we can probably live with that,” he said.

Cardinal Cormac Murphy-O’Connor, the head of the Catholic Church in England and Wales, had said that the closure of his seven agencies would be a “wholly avoidable tragedy”.