The two candidates in the running to replace her - Boris Johnson and Jeremy Hunt - have vowed to succeed where she failed and take Britain out of the European Union, even if that means leaving without an agreement on divorce terms and future relations.
The party leader wrote in a statement to party members on Tuesday: "Whoever becomes the new prime minister should have the confidence to put their deal, or no deal, back to the people in a public vote".
The British Labour Party leader Jeremy Corbyn, who is now promoting remaining into the European Union, challenged the British conservative party to call for another referendum, as we approach the deadline.
Both Tory leadership candidates Boris Johnson and Mr Hunt have said that, if they win the race for No 10, they would seek to renegotiate the terms of Britain's withdrawal, but would leave without a deal if they failed to do so.
In that scenario, the choice on the ballot paper would be between Labour's deal and remaining in the EU, the unions said, and how Labour campaigned in a second referendum would depend on the deal negotiated.
The party has previously rejected Mrs May's deal, but also ruled out leaving the European Union without an agreement and called instead for an election that the party hopes will bring it to power.
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But later they got infuriated as the ceremony was a private affair and just two photos from the event were released. He insisted, "It's frankly hypocritical and they're not private people, they're the Duke and Duchess of Sussex ".
But Jeremy Corbyn wouldn't say what his party's position would be if they won a general election.
So, let's be clear and ensure there is no ambiguity about how remain Labour supporters feel.
On Friday he called on Labour members to sign a declaration, piling pressure on it to become the "party of Remain". It is little more than a weak attempt to get the party leadership out of the Brexit hole it finds itself in, without having to change their core pro-Brexit convictions.
The Guardian adds that the statement does not make reference to the position that Labour would take in the event of a snap general election before Brexit day, or whether under such circumstances if it would still commit to leaving the EU.
But what does this mean in practice, and will it quell the disquiet in the Labour ranks?
But John Mann, a Labour legislator who backs Brexit, said the shift would cost the party support in areas of the country that voted strongly to leave the EU.
"Now, then all those votes get redistributed and then you have a real game on".
Labour MP Hilary Benn, who is also chairman of the Commons' Brexit Select Committee, tweeted: "This is a very significant announcement that will be widely welcomed in the Party. It sounds like we are reserving the right to campaign for remain against our own Brexit deal - that will just sound ludicrous to voters".