In total, 391 MPs voted against the deal and 242 backed it.
Labour has called for no-deal to be "taken off the table" - and said it would continue to push its alternative Brexit proposals, including a customs union. She added, to some cheers from her backbenchers: "I may not have my own voice, but I do understand the voice of the country".
"Her eleventh-hour dash to Strasbourg looked like a desperate ploy to pull the wool over everyone's eyes".
"I understand how incredibly unsettling this is, not just on an economic and security point of view, but also for the thousands of European Union citizens that we have living and working in South Cambridgeshire", she said.
MPs voted down the prime minister's deal by 149 - a smaller margin than when they rejected it by an historic 230 votes in January.
Mrs May said the plan was unworkable, highlighting how any transition period would require a deal with the EU.
She said she was "not frightened" of the people in her Birmingham Yardley constituency who voted to leave, saying if they do not like her views they can vote her out.
Mr Corbyn argued Mrs May has failed, no longer has the ability to lead, and must change her approach.
He has also joined forces with opposition MPs in a parliamentary amendment to stop a "no deal" Brexit, which will be voted on in parliament tonight.
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In a statement, the Commission said it had put forward proposals to try and reassure MPs the backstop "if used will apply temporarily".
The Prime Minister warned a no deal scenario would be "bleak", with a "significant economic shock", the loss of security co-operation with Europe and the prospect of the break-up of the UK as support for Scottish independence and a united Ireland could increase.
Asked if there should be a second referendum, Mr Cameron added: "What happened last night is some people who've always wanted Brexit have voted against it again and this is exasperating for the Prime Minister".
Some of her colleagues around the Cabinet table think it shows she has to tack to a closer deal with the EU.
The MP for Inverness, Nairn, Badenoch and Strathspey said the priority for parliament must be to extend Article 50 and delay the European Union leave date of March 29, in order to allow the decision to go back to the people in a second European Union referendum.
Earlier, Mr Barnier said that talks about the UK's withdrawal from the bloc were now between the British government and MPs.
He said: "Isn't it time she moved on from her red lines and faced the reality of the situation that she has got herself, her government and this country into".
"And that the deal we have negotiated is the best and indeed only deal available".
"That funding is being used to ensure we have preparations for a no deal".