David Cameron is to give MPs a free vote on gay marriage following warnings from Conservative backbenchers that any move to use the whip against MPs could cause "serious divisions" within the party.

The climbdown will be seen as an attempt to avoid splitting the Tory party amid strong opposition in some quarters, despite the prime minister's strong backing for the proposals.

Downing Street suggested on Wednesday that cabinet collective responsibility would apply when same-sex marriage plans are debated in the Commons. "It's a government commitment," said the prime minister's official spokesman.

The BBC reported overnight that "senior party sources" indicated the matter would be put to a free vote, which will allow MPs, including ministers, to vote according to their conscience rather than being directed by party whips.

The decision will remove the pressure on ministers opposed to the same-sex marriage plans. Sources told the BBC they were still confident of getting the measure through.

A formal consultation on how civil marriage will be reformed in England and Wales began earlier this year, but the proposals have proved controversial for some within Cameron's government, including the Northern Ireland secretary, Owen Paterson.

In a letter to a constituent published on the PoliticsHome, Paterson said: "Having considered this matter carefully, I am afraid that I have come to the decision not to support gay marriage."

The children's minister, Tim Loughton, last week made the case for the issue of gay marriage to be a matter of personal conscience "rather than of party political line or institutionalised agenda".

He wrote on his website: "The prime minister has clearly set out his reasons for being in favour of gay marriage and I respect his right to do so. But, I particularly respect his acknowledgement that this should be a matter of personal beliefs and that Conservative MPs at least will be free to make up their own minds.

"As such, I have to say that my instinct is not to support these proposals and, as it stands, I intend to vote against measures to legalise gay marriage".

The defence secretary, Philip Hammond, has said gay marriage was not a priority and the government had to focus "on the things that matter to the people in this country".

Tory MP Stewart Jackson, who resigned as Paterson's former parliamentary private secretary over last winter's vote on whether to hold a referendum on Britain's membership of the European Union, told PoliticsHome on Wednesday that any move to whip MPs would cause "serious divisions".

"Number 10 would be foolish in the extreme to disregard this as a conscience issue," he said.

Gerald Howarth, a defence minister, who was among those to flag up their concerns in recent weeks, told the Daily Telegraph he had been assured that MPs would be allowed a free vote. He said it was "absolutely right and proper" for MPs to be given a free vote.

"These issues are traditionally conscience issues," he said. "There is a long-established principle. I am sure that that will be understood."

David Cameron has personally backed the proposal to allow same-sex couples to marry, arguing at last year's Conservative party conference that "society is stronger when we make vows to each other and support each other". He added: "So I don't support gay marriage despite being a Conservative, I support gay marriage because I'm a Conservative."