Even if the Prime Minister was able to secure the support of the European Union for her proposals, which is highly unlikely, it is hard to see how they will be accepted by the House of Commons, particularly as the Labour Party has one strategy only - to force an early general election.
John Mann has been MP for Bassetlaw since 2001.
He was joined by Heidi Allen, Kenneth Clarke, Jonathan Djanogly, Dominic Grieve, Stephen Hammond, Phillip Lee, Nicky Morgan, Bob Neill, Antoinette Sandbach, Anna Soubry and Sarah Wollaston.
He said: "The margin is closing on these votes and we will keep at it".
The House of Commons gave the go-ahead on Tuesday to the government plan by closely defeating an amendment by several pro-European Union (EU) Conservative and Labour lawmakers.
Meanwhile, US president Donald Trump said Mrs May needed a "carve out" in any Brexit agreement to ensure the United Kingdom can make a deal with the US.
One of the amendments practically says that the United Kingdom should not be collecting tariffs for Brussels unless the European Union does the same for Britain, one of the key ideas in May's original Brexit white paper that was created to keep the Irish border invisible.
MPs in the House of Commons voted 305 to 301 to approve the amendment to the trade legislation.
A furious Mrs May called on the Labour leader to "withdraw" his comments about Vote Leave, adding: "I still contend he made accusations against individual members of this government that were unjustified and he should withdraw them".
Fox called the trade plan "the confident first step that the United Kingdom takes towards establishing itself as an independent trading nation for the first time in over 40 years", which can only happen when it leaves the European bloc.
But his Labour shadow Barry Gardiner said: "The Government's handling of Brexit over the past week has been an utter shambles".
In a withering assessment of the prime minister's handling of Brexit, the former Foreign Secretary told MPs that Britain is heading for "economic vassalage" and warned that "a fog of self-doubt" has descended over the prime minister's premiership.
"Each day that ministers waste arguing amongst themselves increases the risk of the United Kingdom crashing out of Europe without an agreement".
The backbencher is one of a small tranche of Labour MPs who favour a hard Brexit approach.
David Davis, who resigned last week as Brexit Secretary in protest at her negotiating stance, challenged her to publish Whitehall work on a potential free trade deal based on those already secured by the EU.
"This could lead to a damaging and disorderly Brexit because without this Bill passing we would not be able to retain the benefits of more than 40 existing trade arrangements; and neither will we have the means to protect consumers, industries and workers from being undercut by unfairly traded goods in a post-Brexit Britain", she said.
Ms Soubry said the whipping operation during Brexit votes on Tuesday evening had been an "appalling spectacle".
"The proposals on the table satisfy nobody, which is why more and more members of the public know the only way to sort out this political mess is to take back control of the process with a People's Vote on a final Brexit deal".