But Jeremy Corbyn wouldn't say what his party's position would be if they won a general election.
Labour will now challenge whoever wins the Conservative Party leadership race and becomes the next prime minister to put any deal they strike with the European Union to a referendum, "with remain on the ballot, in which Labour would campaign for remain", the party said in a statement.
The shift in stance came as he faced pressure to fully support an anti-Brexit line, with senior members of Labour calling for policy that was more pro-EU.
Lawmakers Boris Johnson and Jeremy Hunt are competing to replace May as Conservative Party leader and prime minister.
Former populist mayor of London, Boris Johnson, was adamant that Britain should leave the European Union on schedule, with or without a deal.
"I want to make it clear that Labour would campaign for Remain against either no-deal or a Tory deal that does not protect the economy and jobs", he said.
Ex-Labour general secretary Lord Triesman is among those to resign, describing how "the experience of life in the party has become sickening".
Tories keep supporting October 31 Brexit while Labour approaches trade unions to gain support for another referendum, blocking no-deal Brexit.
"If we don't get Brexit over the line then we face a haemorrhage of support", Mr Johnson said according to The Telegraph.
As the party website proudly states, "the Labour Party has always been about people", it was formed to give ordinary people a voice and has "sought power in order to improve their lives", becoming one of the most successful social and progressive movements of a generation.
"But I am also very clear that I am representing my constituents and I will continue to do that no matter what because they are the people who put me where I am", she said.
Party member Hilary Benn, who heads parliament's Brexit Committee, said "this is a very significant moment".
"There's no indication whatsoever that voters in my area. have changed their mind", he said.
It comes after the leadership broadly secured the backing of the main trade union bosses - including Unite general secretary Len McCluskey, who had been holding out against a second referendum.
"I'll be your prime minister whoever you vote for", he said.
Any party that proclaims to have the interest of workers at their heart could not have backed a Conservative-led Brexit in good conscience.
The victor of the contest will be decided by a poll of the party's estimated 160,000 voting members and is due to take office later this month. That is something which is surely very important.