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.
May lost the second vote on her Brexit deal on Tuesday, when MPs handed her a humiliating defeat.
In the Commons on Tuesday evening, Labour Party leader Jeremy Corbyn said Mrs May should now call a general election.
David Cameron has warned MPs that failing to rule out a no-deal Brexit would be a "disaster" for Britain.
The UK parliament has again rejected Prime Minister Theresa May's Brexit deal after she secured legally binding assurances from Brussels on the controversial Irish "backstop" - but the changes weren't enough to placate lawmakers.
Some of them believe it's time now to go hell-for-leather to leave without an overarching deal but move to make as much preparation as possible, and fast.
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Battling against her ailment the Prime Minister made a statement after the result of the vote was read out, saying: "I continue to believe that by far the best outcome is the United Kingdom leaves the European Union in orderly fashion with a deal".
While the plans will see tariffs on 87 percent of goods, imported to the United Kingdom cut to zero, the price of some imports, such as meats, will rise. Just three Labour MPs backed the deal.
But ministers said products from the European Union including beef, pork, chicken, butter, cheese and fish would also be subject to import taxes expected to push up prices in the supermarkets from March 29 if there is no deal.
She said that the choices facing the United Kingdom were "unenviable", but because of the rejection of her deal, "they are choices that must be faced".
Ms Trehan said the CBI had reacted with "horror" at the tariffs being announced as a potential option just two weeks away from March 29.
"I know it's incredibly hard but I ask them to trust that at every stage of this, I will absolutely put their needs and our economy in South Cambridgeshire first and that although it feels very turbulent, I do now sense a real chance for optimism that there might be a better, softer Brexit, or a second referendum". The impasse can only be solved in the UK.