The Labour’s leader’s motion of no confidence failed to win support from any Conservative rebels, falling by 325 votes to 306.
It promoted swift calls from other opposition parties and dozens of his own MPs to honour Labour policy agreed at the party’s conference in September to back a so-called people’s vote if a general election could not be secured.
In a joint letter to Mr Corbyn, the Westminster leaders of the Scottish National Party, Liberal Democrats, Plaid Cymru and the Greens said: “We are writing to implore you to adopt as party policy a people’s vote on the final Brexit deal... we believe, as per the motion passed at your party conference, it is only correct that you now move to back a public vote.”
The SNP’s Westminster chief said: “Last night’s historic vote, which saw the UK government humiliated, was a clear indication of the strength of opposition to the Prime Minister’s deal from across the House.
“We must see concessions from the Prime Minister, as well as Jeremy Corbyn, to break the Brexit impasse.”
Green Party MP Caroline Lucas said it was “inconceivable” for Labour to enter talks with the government on how to get its Brexit deal through parliament.
Scottish Liberal Democrat leader Willie Rennie added his voice to the pressure on Mr Corbyn, saying: “There is now nowhere left for the Labour leadership to hide. They must listen to the overwhelming majority of Labour supporters and back a People’s Vote.”
Ian Murray, the Labour MP for Edinburgh South, said: “It was always going to be near impossible for the no confidence vote to be successful, as the parliamentary mathematics remain in the government’s favour.
“That means we can’t force a general election to get rid of this failed government and its austerity programme.
“Labour Party policy is crystal clear – we must now fully support a people’s vote, without delay, to give the public the opportunity to stop the deeper austerity that Brexit will cause.
“There is little time left and the country is crying out for leadership, and we must rise to the occasion.”
Earlier on Wednesday, some 71 Labour MPs and 13 MEPs signed a letter backing a second referendum on withdrawal from the European Union. Organisers said a further 24 Labour MPs had made public statements supporting a second referendum, bringing the total to almost 100.
However, that represents less than half of the parliamentary Labour party who are prepared to publicly back a People’s Vote.
Around 45 of them gathered outside Parliament on Wednesday morning to display a banner reading: “Labour MPs, MEPs, conference and members agree – The people should have the final say.”
The parliamentarians said they backed Mr 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.
However, the party’s core leadership remains reluctant to back a fresh EU referendum, with senior Labour figures indicating they were ready to table repeated no-confidence challenges to Mrs May.
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 said Mr Corbyn should act “immediately” to throw Labour’s weight behind a second referendum.
“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.”