LONDON — Churches were on a collision course with the British government yesterday after the archbishops of Canterbury and York backed their Roman Catholic counterpart by criticizing new gay-rights laws.

The two most senior figures in the Church of England, Rowan Williams and John Sentamu, said in a joint letter to Prime Minister Blair that the consciences of Christians must not be trampled over.

They threw their weight behind an appeal by Cardinal Cormac Murphy-O’Connor for Catholic adoption agencies to be exempted from the new laws so they can turn away same-sex couples.

The cardinal, the head of the Catholic Church in England and Wales, warned Mr. Blair on Monday that without such an exemption, the church would be forced to close its agencies rather than breach church teaching. Scotland’s Catholic bishops made a similar appeal.

Mr. Blair signaled his support for the Catholic agencies to be granted an opt-out from the regulations, due to come into effect in April. But amid reports of growing rifts within the Cabinet, the lord chancellor, Lord Falconer, repeated his opposition to concessions.

In their intervention, which appeared to be designed to bolster Mr. Blair’s position, the two archbishops said speculation about Cabinet splits had undermined negotiations and threatened “to polarize opinions.”

“This does no justice to any of those whose interests are at stake, not least vulnerable children whose life chances could be adversely, and possibly irrevocably, affected by the overriding of reasoned discussion and proper negotiation in an atmosphere of mistrust and political expediency,” they said.

While there was much to be gained by the new laws, which will prevent businesses and other organizations from discriminating against homosexuals in the provision of goods, facilities, and services, there was also much to be lost, the archbishops said.