Jeremy Corbyn faces a revolt from Labour MPs backing a new Brexit referendum, who will launch a drive to rewrite his proposals for the next phase of withdrawal.

The move from three MPs to redraft his strategy, so it ties Labour unambiguously to giving Britain a Final Say referendum, once again thrusts the party’s deep Brexit divisions into the spotlight.

Hours earlier four other Labour MPs had joined Tory counterparts at a press conference, with one accusing Mr Corbyn of “standing in the way” of a people’s vote.

While Mr Corbyn’s office declined to comment on Thursday, the leader’s social media outriders launched a counter-attack on the Labour rebels whom they accused of dishonesty.

Meanwhile doubt has emerged over the viability of a cross-party push by MPs to delay the UK’s withdrawal in order to avoid leaving the EU without a deal on 29 March.

And in Davos, chancellor Philip Hammond warned that a no-deal Brexit – something Theresa May has refused to rule out – would be a “betrayal” of the 2016 referendum result, underlining the split at the heart of the Conservative cabinet.

On Tuesday Ms May will give a statement and table a motion setting out the next steps of her Brexit plan, but because of previous measures approved in the Commons, all MPs will also be able to table amendments containing proposals for what they think the government should do next.

Mr Corbyn has already submitted the Labour Party’s amendment, but it disappointed many backers of the People’s Vote campaign for a fresh referendum because it failed to fully commit the party to backing one.

It would require ministers to find time for MPs only to “consider and vote on options” including renegotiating the withdrawal agreement and also then “legislating to hold a public vote” on any deal that successfully passes through the Commons.

But The Independent understands three Labour MPs – Ian Murray, Angela Smith and Mike Gapes – have now taken the unusual step of tabling amendments to their own party leader’s amendment, in a bid to remould Mr Corbyn’s approach so it backs a new vote immediately.

Mr Murray’s would commit the government to holding a referendum offering a choice between a Brexit deal that guarantees “full participation in the single market”, as previously promised by Labour, and remaining in the EU.

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The amendment submitted by Mr Gapes would “allow the British public an opportunity to have a final say” on leaving the EU, while Ms Smith’s would see ministers legislate for a vote on “whether or not the UK should leave”.

The Independent has run its own Final Say campaign to try and secure a new referendum, with more than 1.1 million people having signed the petition.

While neither Mr Corbyn’s amendment, nor the three amendments to it, stand much chance of being passed in the Commons, the joint push from Labour MPs speaks to a growing frustration on the party’s backbenchers over the ambiguity of the leader’s position as the Brexit clock ticks down to 29 March.

At an event on the steps of parliament earlier in the day Labour and Tory MPs announced they would not table a cross-party amendment for a second referendum because it stood no chance of passing the Commons without Mr Corbyn’s support.

Luciana Berger said: “Regrettably the Labour leadership won’t commit to an achievable policy and yet we know that the majority of Labour voters, supporters and members want a final say on any Brexit deal.

“Yet at a time when Labour should be championing a people’s vote, the leadership avoids answering that call.”

She added: “There are millions of young people in our country that supported the Labour Party at the last general election. Over two million of them were under the age of 18 in 2016. They would today now have a vote. And so many whom I speak to cannot understand why Labour is standing in the way of the younger generation having a say on this.”

Chuka Umunna, who was also at the event, argued that party politics should take a back seat, saying: “The choice is stark and there is no way of escaping from it or postponing making a decision because we are out of time – do you want to facilitate some form of Brexit or give people the power to stop it?”

Meanwhile, Chris Leslie told The Independent: “There really isn’t any excuse now for Labour not fulfilling the conference promise for a people’s vote. An election hasn’t been triggered, so we should be at that stage now.”

Polling indicates Labour voters and members are in favour of a new vote, but the leadership has had to walk a fine line with many constituencies in heartland areas having heavily backed Brexit.

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A separate group of Labour MPs strongly oppose a new referendum, including frontbencher Melanie Onn, who wrote to her constituents saying she would quit her role in Mr Corbyn’s top team if the leadership did back a new vote.

Following the event in the morning Corbyn-backing commentator Paul Mason said the intervention was “daft”, and accused the Labour rebels of “preparing a doomed centrist party”.

Columnist Owen Jones argued that a second referendum amendment would not get through because Labour MPs in Leave seats and Tory MPs would oppose it.

He added, addressing Mr Umunna on Twitter: “You either don’t know the facts or you’re being dishonest. Which is it?”

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The amendment that seems most likely to get thorough the Commons on Tuesday is that written by Labour’s Yvette Cooper, with cross-party backing, that seeks to extend Article 50, delaying Brexit to avoid a no-deal scenario.