Clive Lewis, a shadow minister and supporter of a second referendum, said there "should be no sense of triumphalism" as it was a hard situation for many Labour MPs because of the many varied views on Brexit within the party.
"We are convinced our alternative, which puts jobs and living standards first, could command support in the House of Commons, bring people who voted Leave and Remain together, and be negotiated with the European Union".
Jeremy Corbyn will tomorrow table an amendment to the government's Brexit motion with Labour's five requirements for a "credible alternative plan".
UK Labour and opposition leader Jeremy Corbyn has pledged to back a second referendum after his Brexit alternative was voted down in Commons on Wednesday.
McDonnell, the shadow chancellor, told ITV's Peston that Labour would put forward its own amendment in favour of a second referendum when May puts her Brexit deal to a vote in the House of Commons.
After Wednesday's defeat, he said: "We will back a public vote in order to prevent a damaging Tory Brexit or a disastrous no deal outcome".
"Labour policy was adopted unanimously at the party conference to campaign to give the people the choice of staying in the European Union on the same terms as now or opting for a negotiated form of Brexit".
Shadow Brexit secretary Keir Starmer confirmed that the party's next step would be to support a new parliamentary motion seeking a referendum, with the ballot paper containing remain and a "credible leave option".
At a meeting of the parliamentary Labour party on Monday night, MPs will be told that the move is aimed at preventing "a damaging Tory Brexit being forced on the country".
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Gareth Cattermole via Getty ImagesLarson and Illie chat before the United Kingdom premiere of " Captain Marvel ". The film arrives in cinemas in the United Kingdom and the U.S. on the 8 of March, 2019.
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Opening up the possibility of a delay and removing the immediate threat of a no-deal exit on March 29 marks one of the biggest turning points in the United Kingdom's labyrinthine Brexit crisis since the 2016 referendum vote to leave the EU.
Those involved in talks said the Labour leadership was in favour of a redrafted amendment proposed by backbenchers Peter Kyle and Phil Wilson, which would see the party abstain on the Brexit deal if a second referendum were promised on those terms.
Earlier, Starmer hit out at Theresa May's warning last month that "a second referendum could damage social cohesion" and lead to possible violence on the streets.
If she fails to overturn the 230-vote mauling the Agreement received in January, votes will be held on the following days on blocking a no-deal Brexit on 29 March and extending the two-year Article 50 negotiation process.
The party's own plan for a softer Brexit including a customs union with the EU was defeated once more in a Commons vote yesterday.
Tory MP Ken Clarke rebelled to support Labour's amendment - he was joined by 235 Labour MPs, Liberal Democrat Jo Swinson and three Independent MPs - Ivan Lewis, Jared O'Mara, and John Woodcock.
"That's the time when we will have to put the amendment up".
And a proposal from Conservative backbencher Alberto Costa for a UK/EU treaty to protect expat citizens' rights in the event of a no-deal was passed without a vote.
But Labour said he had effectively been sacked. "That is nowhere near enough to offset the Labour MPs who are not on board for whatever reason", said one MP who meant to back any amendment for a second referendum.