Jeremy Corbyn says opposition MPs will take the first steps towards trying to pass a law blocking a no-deal Brexit when Parliament returns next week.
The Labour leader was speaking after meeting other opposition leaders to discuss ways of averting a no deal.
The move could force the PM to ask the EU for a further Brexit delay, beyond the current 31 October deadline.
A No 10 source accused the MPs of "seeking to sabotage the UK's position" in talks with Brussels.
Those talks were "now making progress", the source added.
Prime Minister Boris Johnson has urged the EU to re-open the withdrawal deal reached with Theresa May, and to make key changes that would allow it to be passed by Parliament.
But he has insisted the UK will be leaving on 31 October even if no new agreement is reached.
Could MPs block no deal through law?
At present, the default position in law is that the UK leaves the EU on 31 October with or without a deal.
MPs opposed to no deal want to pass a new law to change that.
They have already done that once - in April, faced with the possibility of a no-deal exit on the original Brexit date of 29 March, they passed a law forcing Theresa May to ask for an extension to the UK's EU membership.
Repeating that approach would require them to first take control of the parliamentary timetable.
This time round it will be harder because there are limited opportunities do that before 31 October, but one possible option would be as part of an emergency debate - a topical matter added to Commons business at short notice.
MPs plan to apply for an emergency debate as soon as next Tuesday or Wednesday, sources have told the BBC.
It is understood they hope to use the debate to set out a number of dates on which MPs would decide business - meaning Parliament could discuss legislation aimed at stopping no deal.
That could involve cancelling the conference recess in September, although that is not yet confirmed. The MPs are confident the Speaker John Bercow will allow the move.
Tory backbencher and former attorney general Dominic Grieve refused to reveal details of the plan he is backing, but believes enough colleagues on his own benches will join him and the opposition to stop a no-deal Brexit.
"There will be many who will be very, very worried about what the prime minister is doing, but they will also be loyal," he told BBC Radio 4's PM programme.
"But equally... we are facing a deep national crisis and many of my colleagues realise that very well.
"We have to make up our minds - what we are going to say to future generations about what we did during this national crisis?
"I think there are plenty of Conservatives who take the view that a no-deal Brexit would essentially be catastrophic for the country's future and will move to stop it."
What about a no-confidence vote?
Another way of potentially stopping no deal is to try to bring down the Johnson government via a no-confidence vote.
Mr Corbyn had said this was his preferred option, after which he would become interim PM, call a snap election and campaign for another referendum.
However, the Liberal Democrats and some Tory MPs said they would not support any plan that saw Mr Corbyn become prime minister - even on a temporary basis.
Lib Dem leader Jo Swinson said a no-confidence vote "remains a last resort, if you like, to be able to enforce the will of Parliament, but the main proposal is going down the legislative route".
Green MP Caroline Lucas said "the legislative way forward" was "the most secure way to... get rid of that 31 October deadline" and stop a PM "careering towards" no deal.
Mr Corbyn said opposition MPs had agreed to "first" try to avoid no deal using legislation, but using a vote of no confidence to bring down the government at "appropriate time" remained an option.
What other reaction has there been?
The meeting was also attended by the SNP and Plaid Cymru.
SNP Westminster leader Ian Blackford said it had been "positive and productive", adding: "Parliament must grasp this opportunity, unite to stop Boris Johnson shutting down democracy - and be ready to use all mechanisms to block a no-deal disaster, including deploying legislation as a priority."
Plaid Cymru leader Adam Price said his party was "committed to work co-operatively with every other opposition party and do everything in our power to avoid a catastrophic crash-out Brexit".
Mr Corbyn did also invite five Tory MPs opposed to a no-deal exit, but none attended.
The Labour leader has since written to 116 Conservative and independent MPs, who have previously voted against no deal, to ask them to join his efforts.
So how might opposition MPs' attempt to use legislation to prevent a no-deal Brexit work in practical terms?
The first challenge would be to get some Conservative rebels on board, because some in the Labour Party (namely Brexiteers) simply won't back it.
But with Boris Johnson still insisting he can get a deal, it could well be the case that some Tory rebels unhappy with the prospect of no deal would equally be unhappy to rush into anything that would undermine the PM at this stage.
So, it is not at all certain. And in any case, even if Mr Johnson was faced with being forced to do something against his will, he has the option of calling on MPs to vote for an election (under the Fixed Terms Parliament Act).
Yes, Lib Dem Leader Jo Swinson has urged MPs to block that move specifically if Mr Johnson wants to go to the polls only after Brexit.
But under most circumstances, when a PM throws down the gauntlet for an election, it would be an unusual leader of the opposition who doesn't take that challenge.
Brexit Party leader Nigel Farage, speaking earlier in the day, criticised those who took part, saying they were "very out of touch with public opinion" and leaving the EU without an agreement was now "the only acceptable deal".
A No 10 source said: "It's utterly perverse that Corbyn and his allies are actively seeking to sabotage the UK's position.
"This coalition of anti-democrats should be honest with the British public, they are against us leaving the EU no matter what."
Meanwhile, MPs from different parties have signed a declaration pledging to set up an alternative assembly if the PM prorogues - or suspends - Parliament.
Mr Johnson says he has no plans to do this, but has not ruled out such a move to make sure the UK leaves the EU by the end of October.