Labour has tabled a cross-party motion to stop a future prime minister pushing through a no-deal Brexit against the wishes of MPs.
The party plans to force a vote on Wednesday, which would give MPs control of the timetable on 25 June.
Labour says if the motion passes, MPs will be able to introduce legislation to avoid a no-deal scenario at the end of October.
Some Tory leadership hopefuls have said they would leave the EU without a deal.
The government normally controls business in the Commons – but MPs have previously seized control to legislate in favour of extending the Brexit process.
Leaving on a no-deal basis – without any agreement on the shape of the future relationship between the UK and EU – could lead to significant disruption.
The EU has previously said border checks would have to be brought in, affecting things like exports and travel and creating uncertainty around the rights of UK citizens living in the EU and vice-versa.
Labour’s Brexit spokesman Sir Keir Starmer said MPs “cannot be bystanders” while the next prime minister “tries to crash the UK out of the European Union without a deal and without the consent of the British people”.
“That’s why we are taking this latest measure to end the uncertainty and protect communities across the country,” he said.
“My challenge to MPs who disagree either with a no deal Brexit or proroguing Parliament is to back this motion and act in the national interest.”
Leadership candidates Dominic Raab and Esther McVey have both said they would consider shutting down Parliament early – proroguing – in order to drive through no deal.
The motion has cross-party backing, including from one Tory MP – Oliver Letwin – who is support Michael Gove in the Tory leadership contest.
It has been signed by Jeremy Corbyn, SNP Westminster leader Ian Blackford, Lib Dem leader Vince Cable, Plaid Cymru Westminster leader Liz Saville-Roberts and former Green Party leader Caroline Lucas.
International Trade Secretary Liam Fox told the BBC the move was “typical of the current Labour Party”, saying: “Jeremy [Corbyn] wants to be a Remainer in the south and a Leaver in the north.”
“Is it (the Labour Party) actually trying to block Brexit now?” he asked.
“If Labour tomorrow wants to make no deal impossible, they are making revocation [of Article 50] and staying in the EU a possibility.”
Justice Minister Robert Buckland called it “parliamentary game-playing”, asking: “What is the point of all this sound and fury?”
Leadership candidate Mark Harper, who earlier said it was “not possible” to leave on the terms of a new deal by the existing deadline of 31 October, said Labour’s plan could carry if just three Tories back it.
Change UK MP Chris Leslie said Tory leadership candidates “who think they can just shut down the Commons” to deliver a no-deal Brexit should “wake up and realise there is a cross-party majority of MPs who just will not let this happen”.
And Labour MP Ben Bradshaw said all MPs who “profess to oppose prorogation” for no deal should back the motion.
“It could be our only insurance policy,” he aded.
Ex-director of legislative affairs at No 10, Nikki da Costa called the move “extraordinary”.
It came after shadow chancellor John McDonnell insisted the party was not in “turmoil” over its Brexit stance.
He was responding to questions about a heated Parliamentary Labour Party (PLP) meeting on Monday in which Mr Corbyn faced criticism from his MPs.
A number of MPs expressed concerns that it had now become “normalised” for Labour voters to back other parties over Brexit, while others strongly criticised Mr Corbyn’s handling of anti-Semitism.
Speaking at the Times CEO summit, Mr McDonnell said he welcomed lively debate.
“I would rather have people get up and say, ‘This is what I feel,’ passionately, rather than sneak away to the corners,” he said.
Asked whether his party was in turmoil over Brexit, he replied: “It’s not turmoil.”
He said the party had promised to respect the referendum result in its manifesto and now, after failing to secure a deal with the Conservatives in cross-party talks, the situation meant “most probably going back to a public vote” – his preference being a general election.
But Labour MP Anna Turley said colleagues were “shell shocked” afterwards, such had been the level of anger expressed.
“I think the cleaners are probably still mopping up the blood,” she added.
Ms Turley, who did not attend Monday’s meeting herself, is calling for a “firmer position on Brexit” from the party leader – with her preference being for a confirmatory vote on any deal agreed between the UK and the EU.
She told the BBC’s Politics Live programme colleagues who had been present made clear it had been a “messy and difficult” meeting.
Mr McDonnell also said he was frustrated that Alastair Campbell was expelled more swiftly than some accused of those within Labour accused of anti-Semitism, after the former spin doctor for Tony Blair voted for the Liberal Democrats in the European elections.
“I was annoyed, but here’s the irony – the process that removed Alastair Campbell was brought in by New Labour under Alastair Campbell and Tony Blair,” the shadow chancellor said.
“We should review that procedure, it doesn’t work.”
After the PLP meeting, a spokesman for Mr Corbyn said there were strong feelings about Brexit and the shadow cabinet would discuss Labour’s “evolving” position on Tuesday.
“The PLP [the parliamentary Labour Party] is generally quite a robust meeting,” he said. “The PLP is very passionate about lots of issues not just about Brexit. That’s what we would expect.”