But while it appears there is no Commons majority for any form of Brexit, there is nearly certainly a majority which would attempt to block no deal.
The news came as Tory MPs will today [Monday] raise concerns about a secretive committee run by unelected officials with the power to write new laws affecting Britons for years after Brexit as a result of Mrs May's deal.
'It is right to vote down this bad deal and that in doing so we will unlock a better future for our party, our country and its people.
Esther McVey, Priti Patel, Owen Paterson, Dominic Raab, John Whittingdale, Mark Francois, Steve Baker, Shailesh Vara and Suella Braverman also backed the letter.
In a significant shift of tone apparently created to win over hardline Brexiteers who have set their faces against Mrs May's deal, Mr Hunt warned that defeat next week would not necessarily provide MPs with the opportunity to choose their preferred version of Brexit.
He used an article in the Sunday Telegraph to urge MPs to vote down May's "bad" deal to send a message to Brussels that the United Kingdom "will not be bullied".
Mrs May postponed the vote last month in the hope of winning more support but she is still predicted to lose in tomorrow's vote.
She is expected to say: "I ask MPs to consider the consequences of their actions on the faith of the British people in our democracy".
Writing in the Sunday Express, Mrs May said: "You, the British people, voted to leave".
May's office also said it was "extremely concerned" about reports that some MPs would try to seize control of Brexit negotiations if the agreement May's Government reached with the European Union is defeated. "Or else force them to vote again".
Ian Blackford said MPs must take control of the Brexit process and ensure a no-deal outcome is avoided.
"We all have a duty to implement the result of the referendum".
Pressed on what happens if the deal is defeated, Mr Barclay said he suspected the Commons would support something "along the lines of this deal" but declined to speculate on whether the government had a Brexit "plan B" lined up.
He told BBC Radio 4's Westminster Hour: 'I would not stay in office, I would stand in front of that no-deal juggernaut.
"I'm saying this would be [an] incredibly damaging breach of trust and it would also be very bad for Britain's reputation overseas, having chose to leave the European Union, if we in the end for whatever reasons found we weren't able to do it".
"I don't like the prospect of a no-deal".
The Labour leader said people should "see what happens" on Tuesday, when Mrs May's controversial Withdrawal Agreement is put to a vote in the Commons, but said his party would table a confidence motion "at a time of our choosing".
Brexit Secretary Steve Barclay told the BBC's Andrew Marr Show, after he was asked if the plot was real, that there was a "growing risk" that Parliament could frustrate Brexit.