Ms Flint, who voted against the Prime Minister’s initial deal in January, gave the deal her backing but it was voted down by 391 to 242 – a smaller defeat than when they rejected it two months aho but still humiliating as the clock ticks down towards the March 29 deadline for the UK to leave the EU.
The PM said she ‘profoundly regrets’ that her deal was voted down but added Tory MPs will get a free vote on a no-deal Brexit today, meaning they can vote with their conscience rather than follow the orders of party managers.
If the Commons declines to approve a no-deal Brexit a vote on extending Article 50, the legal mechanism taking the UK out of the EU on March 29, will take place on Thursday, said Mrs May.
Announcing the free vote, she told MPs: "This is an issue of grave importance for the future of our country.
"Just like the referendum there are strongly held and equally legitimate views on both sides.
"For that reason, I can confirm that this will be a free vote on this side of the House."
She said that the choices facing the UK were ‘unenviable’, but because of the rejection of her deal, ‘they are choices that must be faced’.
Labour leader Jeremy Corbyn said the prime minister should now call a general election.
The EU's Chief Brexit negotiator Michel Barnier said in a tweet: "The EU has done everything it can to help get the Withdrawal Agreement over the line. The impasse can only be solved in the UK. Our 'no-deal' preparations are now more important than ever before."
All of Sheffield’s MPs – Louise Haigh, Sheffield Heeley; Paul Blomfield, Sheffield Central; Jared O’Mara, Sheffield Hallam; Clive Betts, Sheffield South East; Gill Furniss, Brightside and Hillsborough and Angela Smith; Penistone and Stocksbridge, who quit the Labour party last month to join the Independent Group, voted against the deal.
But Sir Kevin Barron, MP for Rother Valley, Ms Flint both voted in favour of Mrs May’s deal, along with fellow Labour colleague John Mann, who represents Bassetlaw.
Ed Miliband, Doncaster East MP; Sarah Champion, Rotherham MP; John Healey, MP for Wentworth and Dearne, and Barnsley MP Dan Jarvis voted against the deal.
Doncaster Central MP Rosie Winterton is deputy speaker and so was unable to vote.