For the English Anglican church, English gay marriage law means that it will stop performing marriages for the state.

From the Guardian:

The threat of an unprecedented clash between church and state over the issue of gay marriage has opened up after the Church of England delivered an uncompromising warning to the government against pressing ahead with controversial proposals.

Introducing same-sex marriage could lead to the church being forced out of its role of conducting weddings on behalf of the state, the church claimed in a potentially explosive submission in response to the government's consultation on gay marriage, which closes on Thursday.

The submission's warning of a potential clash between canon law – that marriage is between a man and a woman – and parliament is likely to put pressure on the prime minister, David Cameron, who has spoken out in support of gay marriage and already come under fire from supporters of the proposals for allowing a free vote amongst Tory MPs.

In a 13-page submission, the church says it cannot support the proposal to enable all couples, regardless of their gender, to have a civil marriage ceremony.

"Such a move would alter the intrinsic nature of marriage as the union of a man and a woman, as enshrined in human institutions throughout history," it says.

"Marriage benefits society in many ways, not only by promoting mutuality and fidelity, but also by acknowledging an underlying biological complementarity which, for many, includes the possibility of procreation."