Some 71 Labour MPs and 13 MEPs have signed a letter backing a second referendum on withdrawal from the European Union.
The MPs said they backed leader Jeremy Corbyn's tabling of a no-confidence motion in the hope of forcing an early general election, but said if this did not succeed the party should "unequivocally" back a public vote.
The move intensifies pressure on Mr Corbyn to move quickly, after senior Labour figures indicated that the party was ready to table repeated no-confidence challenges to Mrs May if Wednesday's vote does not succeed in ousting her.
A motion passed at the party's conference last autumn made clear that a general election is Labour's priority, but stated that if this was not possible, the party would "support all options remaining on the table, including campaigning for a public vote".
Senior backbencher Louise Ellman told the Press Association that Mr Corbyn should act "immediately" to throw Labour's weight behind a second referendum if Wednesday's vote failed.
"We've got the no-confidence motion today," said the Liverpool Riverside MP. "If that doesn't carry, Jeremy should immediately call for a second referendum and start taking the moves to make that happen.
"We shouldn't have any further delay. The clock is ticking. It's just over 70 days to go before we actually leave the EU. We can't afford to do that, so Jeremy must act now."
Tottenham MP David Lammy told BBC Radio 4's Today programme it was time for Mr Corbyn to move, warning: "If he vacillates and sits on the fence, I'm afraid he is going to get splinters in places he doesn't want.
"There is is definitely momentum with Members of Parliament who now see that this is stuck in our Parliament and think he should put it back to the British people."
Among signatories to the letter were MPs from Leave- and Remain-backing constituencies from all parts of Britain, including the party's former acting leader Dame Margaret Beckett, ex-ministers like Ben Bradshaw and Chris Bryant, and former leadership contender Owen Smith.
Organisers said a further 24 Labour MPs had made public statements supporting a second referendum, bringing the total to almost 100.
On the morning after the historic defeat of Mrs May's Withdrawal Agreement in the House of Commons, around 45 of them gathered outside Parliament to display a banner reading: "Labour MPs, MEPs, conference and members agree - The people should have the final say."
Bridget Phillipson said she recognised the anger about the state of the country which lay behind the 60% Leave vote in her Houghton & Sunderland South constituency.
But she said it would be much harder for Labour to achieve its goals of ending austerity, reducing child poverty and helping working people if the UK left the EU.
In a statement, the MPs and MEPs said: "We must try and remove this Government from office as soon as possible.
"But the removal of the Government and pushing for a general election may prove impossible, so we must join trade unions, our members and a majority of our constituents by then unequivocally backing the only logical option to help our country move forward: putting the decision back to the people for a final say, in a public vote, with the option to stay and keep the deal that we have."
The statement said the UK was in "an unprecedented and perilous moment in our history" and accused Prime Minister Theresa May of running down the clock on Brexit in a way that amounted to "gambling with the jobs and livelihoods of our constituents".
"We now face a moment of national crisis, where the facts and the views of many people have changed - and are continuing to change," they said.
"It is now clear renegotiation is not a realistic prospect. No-deal would be a catastrophe which we must resolutely oppose. The Government should seek an extension to Article 50 to provide time for Parliament to find a way forward."
They were harangued by pro-Brexit protester Colin Grostate, from Ramsgate, who brandished a Conservative Party membership card as he loudly accused them of being "liars".
Dressed in a yellow high-visibility jacket bearing the slogan "Clean Brexit - No Deal", he confronted Mitcham & Morden MP Siobhan McDonagh, telling her: "I'm just a little man on the side with a vote which you don't care about. I don't want a second vote."
Ticket barriers at Westminster's Underground station were plastered with adverts from second referendum campaigners, reading "The only way forward is a People's Vote."
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