The chief executive of gay rights charity Stonewall has responded cautiously to claims David Cameron may fast-track equal marriage legislation. Ben Summerskill also believes this week’s Church of England vote on female bishops could affect the equal marriage campaign.

Writing in the Guardian, Mr Summerskill suggested the prime minister may have wanted to send out a message in response to the Church of England’s failure to agree on approving women bishops.

“If he’s doing so because he thinks the most obsessed fundamentalists might be wrong-footed, he underestimates their willingness to be outraged about almost anything,” said Mr Summerskill.

He went on to say of David Cameron:  “But if he’s pushing forward because, in rejecting women bishops, the Church of England now appears to have holed below the waterline any claim it has credibly to represent 21st-century Britain, the prime minister may have a good point”.

Several commentators have argued Tuesday’s vote by the General Synod means Anglican opponents of gay equality will find it harder to gain political sympathy.

While 324 synod members voted for women bishops, church voting rules meant 122 votes against were enough to block the reform.

The Reverend Canon Robert Cotton of Westcott House theological college in Cambridge said after the vote: “We have made David Cameron’s job getting gay marriage through much easier — why should he take the Church of England seriously when it seems interested only in looking after its own?”

On Friday, the Department for Culture, Media and Sport (DCMS), which houses the government department responsible for responding to the public consultation on equal marriage, sought to downplay Thursday’s speculation about a faster timetable.