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Boris Johnson has come to the aid of David Cameron’s plans for gay marriage by recording a YouTube video in favour of the plan.

In his 38-second film, the Mayor says marriage rates are going up in London and nobody should be denied the benefits.

Support from Mr Johnson, who is arguably the most popular and successful Conservative in the country, is a godsend to the Prime Minister, who is facing a bitter Tory split on the issue and a revolt at the autumn party conference.

Allies of Mr Cameron argue that Mr Johnson’s successful re-election in May for a second term is proof that the Tory Right is wrong to assume that allowing same-sex marriage is electoral suicide.

Mr Johnson’s true intentions were probably not to help out the Prime Minister, who is nowadays a fierce rival, but to honour a promise made two months ago to record a video to support the Out4Marriage pressure group.

Last week, Labour and Liberal Democrats on the London Assembly challenged him by asking when he would fulfil the pledge, prompting him to record the film on Friday.

The Mayor does not actually use the word “gay” and begins by boasting about crime reduction in London, which is an issue more likely to please Tory Right-wingers if they come across his video on YouTube.

In the video he says: “Hi folks, I’m Boris Johnson, I’m Mayor of London. One of the amazing things about London is that it’s not only got a declining crime rate, declining murder rate, more theatres than New York, less rainfall than Rome but it’s also one of the few places in the country where the rate of marriage is actually increasing and I see absolutely no reason why that happy state should be denied to anybody in our country. And that’s why I’m supporting the Out4Marriage campaign.”

A No 10 source said: “We support gay marriage and welcome others supporting it too.”

Benjamin Cohen, of Out4Marriage, said: “Boris Johnson was one of the first senior Conservative politicians to back the idea of equal marriage, doing so in public before the Prime Minister.

“He like many has been on a journey when it comes to this issue and we welcome his support for Out4Marriage as we edge closer to the publication of draft legislation to allow gay couples to marry.”

Mr Cameron pledged to enact gay marriage two years ago and a formal consultation is under way. However, it was not mentioned in the Queen’s Speech which raised fears among campaigners that he was getting cold feet. The Cabinet is divided on the issue.