The PM's deal will be put to another vote next week, just 15 days before the country is due to leave the European Union on 29 March, after MPs including four rebellious Cabinet members (Amber Rudd, inset) voted to permanently rule out No Deal Brexit.
With Brexit due in 15 days and no divorce deal yet approved, the House of Commons voted 412-202 to ask the bloc to postpone Britain's exit until at least June 30.
The vote makes it likely that the March 29 departure date set down in law, which May has repeatedly emphasised, is likely to be missed, although it is unclear by how long.
If her deal is rejected for a third time and is not approved by Wednesday, the government will ask for a longer extension. She was wheeled into parliament having delayed the date of baby Raphael's birth by a day so she could join MPs voting against Mrs May's deal when it was first thrown out by MPs.
"The PM said the choice was between her deal and no deal".
But lawmakers also rejected a call to use that time to hold a second Brexit referendum - a blow to the hopes of a large swath of Britons who still dream of keeping their European identities. Most opposition Labour lawmakers did not back the measure and even campaigners for a so-called People's Vote said the time was not yet right for Parliament to vote on the matter.
The move comes as Theresa May battles to build support for her European Union withdrawal deal. But she has made clear her plan is still on the agenda, despite twice being rejected by an overwhelming majority in Parliament, in January and again this past Tuesday.
If May fails to win parliamentary approval for her deal by March 20, the Brexit delay could be extended beyond three months.
The EU must increase pressure on Britain to move forward on its exit from the bloc, the European Parliament's Brexit coordinator told German television on Thursday, after the vote in the Commons.
Pound has swung more wildly this week than at any point since 2017, rising from below $1.30 to a nine-month high of nearly $1.34 as investors bet Britain would avoid a no-deal Brexit.
"Of course we understand that Brexit is a major issue for each and every one of us, but we would like to have more time to have a debate and allow the public to have more of a say in how to solve the Brexit conundrum". I have consistently voted and acted to support the Prime Minister's plan to leave the European Union.
"But I gave the prime minister my ideas on how to negotiate it and I think you would have been successful".
"She didn't listen to that and that's fine - she's got to do what she's got to do". But if there seems little sign the stalemate is ending, some may argue it is better to end uncertainty for business and go to a "no deal" Brexit, for which they have prepared. Brexit supporters say that, in the longer term, it would let Britain forge trade deals across the world and thrive.
The DUP's Westminster leader, Nigel Dodds, has stated that May's government has failed to implement what was agreed and included in paragraph 50 of the joint report in December 2017, which stated the assembly would be able to veto any new regulatory difference.
Following the vote European Council president Donald Tusk indicated that the EU may be ready to offer a lengthy extension to negotiations if the United Kingdom wants to "rethink its Brexit strategy and build consensus around it".
"We take note of the votes in the House of Commons this evening", the spokesman said.
Nearly two thirds of Tory MPs voted against their government's motion to delay Brexit.
The Democratic Unionist party is locked in intensive talks to try to reach an agreement to allow it to back Theresa May's Brexit deal, including with the attorney general, Geoffrey Cox, and the chancellor, Philip Hammond.