"I want to make it abundantly clear to those of my honourable friends who are thinking of voting against the prime minister's deal, which I shall be supporting, that the majority in this house, if it is expressed tonight, will sustain itself, and we will not allow a no-deal exit to occur at the end of March".
Twenty Conservative MPs rebelled against the government and their own party, including former cabinet ministers Michael Fallon, Justine Greening, Dominic Grieve, Ken Clarke and Oliver Letwin.
But supporters said the vote - of 303 to 296 - showed there was now a clear majority of MPs who would oppose a no-deal if Mrs May can not, as many expect, win the backing of the Commons for her agreement.
The British government on Tuesday ruled out seeking an extension to the two-year period taking the country out of the European Union as Prime Minister Theresa May continued to seek further concessions from the EU ahead of a crucial parliamentary vote next week on her Brexit deal.
"I'm anxious we could come to the crunch and parliament will not have the powers to stop [no deal] happening" Cooper said in the aftermath of the vote, adding: "I think we have a responsibility not to just stand by".
"Theresa May must now rule out no deal once and for all", he added.
This is a breaking news story and will be updated.
If and when the prime ministers's plan is voted down on Tuesday, MPs feel they can not wait potentially until 12 Feb for the next vote.
Meanwhile MPs narrowly passed an amendment yesterday that seeks to stop the government enacting a no-deal Brexit by hampering it from taking financial measures to mitigate any economic headwinds caused by leaving the European Union without a deal - the alternative ministers have claimed will happen if parliament rejects May's deal.
Mrs May has said the United Kingdom will be in "uncharted territory" if the agreement is rejected and this could put Brexit at risk - although she has not ruled out asking MPs to vote a few times.
Downing Street confirmed that the so-called "meaningful vote" is scheduled to take place on Tuesday January 15, with the Prime Minister wrapping up five days of debate kicked off on January 9 by Brexit Secretary Stephen Barclay.
But she was warned the attitudes of Tory Brexiteers had hardened, with Boris Johnson stating that a no-deal Brexit was closest to what people voted for in the referendum.
Cabinet Office minister David Lidington, seen as Mrs May's effective deputy, this morning issued another frantic plea for critics to get behind her plan. The EU has signaled it may try to allay the fears of May's critics but will not renegotiate the deal.
"But there's little point in extending if all we are going to do is seek another tweak or twiddle to the Withdrawal Agreement. I think it's those kind of assurances we are happy to give".
French European affairs minister Nathalie Loiseau urged reluctant British lawmakers to back the deal, which lays out things like Britain's future financial obligations, the rights of citizens hit by Brexit and steps to keep goods flowing freely across the Irish border.