Campaigners for gay marriage to be legalised received a boost today when Theresa May, the Home Secretary, declared her full support for the move.

In a rebuff to Conservative MPs who oppose same-sex marriage, Mrs May, who is also the Minister for Women and Equalities, declared that “marriage should be for everyone.”

Her intervention in the heated Tory debate on the issue significant. Until now, the running on the issue has been made by Lynne Featherstone, the Liberal Democrat Equalities Minister at the Home Office.

Although her department is still conducting a consultation exercise on same-sex civil marriage, Mrs May endorsed the Out4Marriage campaign. In a video filmed for the group, she admitted there are “strong views on both sides of this argument”.

She said: “I believe in marriage. I believe marriage is a really important institution, it's one of the most important institutions we have. Marriage binds us together, it brings stability, I think marriage makes us stronger. But I believe also in commitment and in fidelity in marriage, I think these are good things and we should enable them to flourish.”

The Home Secretary added: “That's why I believe if two people care for each other, if they love each other, if they want to commit to each other and spend the rest of their lives together then they should be able to get married and that marriage should be for everyone.”

The group hopes that Mrs May’s backing will draw a line under speculation that the Government might backtrack after pressure from Tory backbenchers to drop the proposal. Their demands for ministers to focus on bread-and-butter economic issues have grown since the party suffered heavy losses in this month’s local elections.

Mike Buonaiuto of Out4Marriage.org said: "We look forward to working with the Home Secretary and the Government as a whole to ensure that the final legal discrimination against lesbian, gay, bisexual and transgendered people is removed from the statute book. We are equally delighted that in just a two weeks, Out4Marriage has gained support from senior Conservatives, Liberal Democrats, Labour and Green politicians."

In an attempt to placate Tory MPs, Downing Street has confirmed that they will be allowed a free vote when a Bill to equalise civil gay marriage is brought forward because the issue is a matter of personal conscience.

Opponents believe about 70 Tories may vote against the idea and others could abstain. But the measure is likely to be approved because it enjoys the support of most Labour and Liberal Democrat MPs.

Today Labour criticised the Government for dragging its feet on the move. Angela Eagle, the shadow Commons Leader, said the free vote had been granted because David Cameron faced a Cabinet revolt on the issue. “This means that the government’s flagship policy on equal rights will only become law with Labour support,” she said.