Jeremy Corbyn is battling to calm a growing Labour civil war over his refusal to support a fresh Brexit referendum, as some of his MPs threatened to quit the party in protest.

The Labour leader was forced to justify his intentions after his new offer to help Theresa May deliver Brexit triggered accusations that he had torpedoed his party’s policy of keeping a public vote on the table.

Amid growing tensions, Mr Corbyn wrote to party members to insist that party backing for a Final Say referendum remained an option – hours after furious Labour MPs accused their leader of helping enable Brexit.

The backlash was triggered when Mr Corbyn wrote to Ms May on Wednesday evening offering continued discussions in “constructive manner” with the aim of “securing a sensible agreement that can win the support of parliament and bring the country together”.

Labour would support an exit deal if five conditions were met, he said, including a customs union with the EU and guarantees on workers’ rights.

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The move infuriated anti-Brexit MPs pushing for Labour to back giving the public the final say on Brexit, with two suggesting they were considering quitting the party over the issue.

Owen Smith, who stood against Mr Corbyn for the party leadership in 2016, said Labour should be opposing the “disaster” that is Brexit.

Asked if Mr Corbyn’s letter paved the way for Labour MPs to support a Brexit deal put forward by Ms May, he told BBC 5Live: “I think that’s probably right. My fear is that this is the leadership rolling the pitch for accepting a version of Theresa May’s deal, and I think that will be at odds with our values and damaging to our country and damaging to the politics that we’ve traditionally believed it.

“Brexit is a right-wing ideological project and we should be opposing it on those terms.”

Asked whether he would resign over the issue, Mr Smith admitted he was “considering” whether he could continue as a Labour MP, saying: “I think that’s a very good question and I think it’s something that I and lots of other people are considering right now.”

Pushed on whether he could quit if Ms May’s Brexit deal is passed next month, he replied: “That’s possible.”

Liverpool Wavertree MP Luciana Berger, another supporter of the campaign for a Final Say referendum, also refused to rule out leaving the party.

Appearing on ITV’s Peston, she did not deny being part of discussions about a breakaway party and admitted there was “a disaffection with the lack of leadership we’re seeing on all sides”.

Asked whether she might quit, she said: “I’m focused on Brexit – that’s my responsibility as a constituency MP.”

She added: “There’s many people that have many different challenges, not just Brexit, in terms of seeing leadership from all the main political parties.”

It comes after Chris Leslie, another leading advocate of a fresh referendum, hinted that he could also quit, telling The Observer: “A lot of people’s patience is being tested right now. I think there are some questions we are all going to have to face, especially if Labour enables Brexit.”

With the party threatening to be engulfed by civil war over Brexit, Labour officials emailed MPs insisting they had not ruled out backing another referendum.

In a briefing document justifying Mr Corbyn’s decision to reach out to Ms May, they wrote: “This is consistent with our conference policy and the frontbench amendment we set out on 29 January: that made clear there are two credible options that Labour could support to prevent no deal and break the current impasse – either a close economic relationship or a public vote. This letter sets out in more detail the first of those options. It does not rule out the latter.”

Sir Keir Starmer, the shadow Brexit secretary, also sought to quell the growing backlash, telling the BBC: “What this letter does is to set out that the prime minister needs to abandon her Brexit red lines. It does not rule out the option of a second referendum – a public vote – and Jeremy Corbyn is going be writing to members today to reassure them about that.”

Sir Keir is seen to be more favourable than Mr Corbyn’s inner circle to the idea of Labour backing another referendum.

Defending his offer to work with Ms May, Mr Corbyn told Sky News: “Half of our trade is with Europe, a lot of our manufacturing industries are very frightened and very worried at the moment that on 29 March there will be a cliff edge. There cannot be a cliff edge and we will do everything we can in parliament to prevent this cliff edge exit.”

Guy Verhofstadt: 'We welcome the letter sent by Jeremy Corbyn'

In an email to party members, he said: “Labour can and must take a lead in bringing our country together.

“We are convinced that our sensible alternative, set out in the five demands in my letter, could both win the support of parliament and bring together those who voted Leave and Remain.”

He added: “Theresa May is unable to reach a sensible deal because it would split the Tories – and we will never vote for a bad Tory deal.

“If parliament is deadlocked, then the best outcome would be a general election. Without it, we will keep all options on the table, as agreed in our party conference motion, including the option of a public vote.”

That was not enough to reassure supporters of a Final Say referendum, with MPs condemning Mr Corbyn’s offer to work with Ms May if she agreed to meet Labour’s five conditions.

Writing exclusively for The Independent, Streatham MP Chuka Umunna said: “These tests are nonsense and Labour’s policy is all over the place.

“Above all, the letter makes no mention of referring this back to the people. The spirit of Labour’s conference policy was that if we couldn’t get an election, Labour would commit to referring this issue back to the people.”

He added: “The leader and those around him have made it clear they have no interest in going there at all. He has also tacitly given a green light to those who not only won’t support a People’s Vote but are also happy to thwart the House of Commons’ ability to stop the UK crashing out of the EU without a deal in 50 days.

“That is the harsh reality of what we have learned these past couple of weeks. The party won’t be forgiven by the next generation.”