"Since her Brexit deal was so overwhelmingly rejected, the Prime Minister has recklessly run down the clock, failed to effectively negotiate with the European Union and refused to find common ground for a deal Parliament could support".
After the voting, Mrs May said that MPs will vote on Thursday on an extension to Article 50, which could involve a short delay to implement a deal agreed in the next few days or a longer delay if no agreement is reached.
Labour's Sir Keir Starmer said that after the 149-vote defeat of her Withdrawal Agreement on Tuesday, Mrs May's mantra of "my deal or no deal" should be "dead and buried".
Her exchanges with Corbyn involved the Labour leader repeatedly urging the prime minister to outline a new plan for Brexit, and to consider backing the Labour proposal, under which the United Kingdom would stay in some form of customs union.
She added at Prime Minister's Questions: "He has nothing to offer this country".
Mr Loughton tweeted: "This evening I have held my nose and voted for the Government's deal with the Attorney General's extra assurances with no enthusiasm but with a greater fear of the damage that prolonged uncertainty and chaos could cause but I fear with little chance of it going through".
MPs will vote tonight on whether they want to leave the European Union without a withdrawal agreement and Political Declaration - a no deal Brexit.
Ireland and the 26 other European Union states would also need to agree unanimously to any extension to the Brexit negotiation process.
She was among those who voted to keep the scenario on the table tonight.
Labour has also said it won't vote for May's deal, as Jeremy Corbyn accused the government of trying to "fool" its own backbenchers - and the British people.
In a statement, the Commission said it had put forward proposals to try and reassure MPs the backstop "if used will apply temporarily".
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".
Leading Tory Remainers and Brexiteers, including Dominic Grieve and Boris Johnson, have suggested the prime minister's deal is now "finished" and other options must be brought forward.
If MPs reject no-deal as most Westminster observers expect, a third vote will follow tomorrow on whether to authorise Mrs May to request an extension of the two-year Article 50 negotiation process.
MPs rejected by 374 votes to 164 an amendment from members of the Malthouse Compromise group of Tories from both Leave and Remain wings of the party.
"We owe it to the country to provide them with a government that can govern", he said.
"That funding is being used to ensure we have preparations for a no deal".