Friday was meant to be the day the United Kingdom left the bloc after more than 40 years of membership and nearly three years of wrangling over the divorce.
May had offered on Wednesday to resign if the deal passed, in a bid to win over eurosceptic rebels in her Conservative Party who support a more decisive break with the European Union than the divorce her deal offers.
May said MPs would continue on Monday to try and "see if there is a stable majority for a particular alternative version of our future relationship with the EU", adding that any plan would also require parliamentarians to back the withdrawal agreement.
He added that Britain needed a "revolution" so that Parliament "reflects the will of the people".
UK PM Theresa May had staged the third Brexit vote as the final opportunity to ensure Britain's divorce with European Union, however, in a special sitting of the UK House of Commons, UK lawmakers voted 344-286 against the Theresa May's obsessive withdrawal agreement.
The vote left Britain's withdrawal from the European Union in turmoil.
"Since it took 2 3/4 years for the government to get what it had negotiated defeated three times, it's a little bit harsh on Parliament, when it started the process last Wednesday, for not having immediately solved the problem in 24 hours", Benn said.
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However, speculation is also growing that the only way out of the impasse is a snap election.
The letter, signed by 170 members of the Prime Minister's party, called on her to bring her deal back to Parliament for a fourth vote, with the threat of a general election if it is rejected again, the newspaper said. Nigel Farage and Tommy Robinson were among those who addressed the crowds of March To Leave demonstrators who arrived in the capital today after making the 14-day trip from Sunderland. "Why would you want to hold your nose and vote for something that was so against your instincts and against the interests of the British people?" rebel Tory MP Sir Christopher Chope told the House.
He said: "I'm convinced at that after spending a lot of time meeting with and talking to officials in Europe".
But like all things in British politics these days, it wasn't that simple. Propped on the stage beside him was a coffin with May's face on it and the word "democracy".
Corbyn raised this possibility knowing that most Labour MPs are resolutely opposed to him becoming prime minister.
Later in the evening there was a small stand-off between Robinson supporters and police, as around 100 supporters protested outside May's office shouting "We want Brexit!"
The political morass has left Britons on both sides of the debate frustrated and angry.
"It is absolutely disgusting what is happening", he said."Be warned - this is just the beginning of a mass uprising if we get betrayed by the politicians".