Mr Mundell did not deny this yesterday, saying: 'I don't comment on private conversations I've had with the Prime Minister, but what I've said to her repeatedly and what I've said to Cabinet is that a No Deal Brexit is a very bad outcome for Scotland and the United Kingdom and we must do everything we can to avoid that'.
Philip Lee, who quit as a justice minister over Brexit, had been named as a potential future defector to the Independent Group.
The Labour MPs had cited left-wing leader Jeremy Corbyn's handling of both Brexit and rising anti-semitism within the party since he came to power in 2015.
Announcing their resignations, the three Tories - Sarah Wollaston, Heidi Allen and Anna Soubry - told the Prime Minister in a statement, "We no longer feel we can remain in the Party of a Government whose policies and priorities are so firmly in the grip of the ERG and DUP".
"The government which I am supporting implementing a No Deal Brexit - what would I do?"
The "backstop", an insurance policy to prevent the return of a hard border between the British province of Northern Ireland and European Union member Ireland if the Brexit negotiations fail to come up with a future relationship to prevent it, is the main point of contention in ongoing talks with Brussels.
It remains possible that Britain will crash out with no deal, or that Britain will seek a delay beyond the March 29 deadline, or that more negotiations will be undertaken, or that citizens will be asked to vote again on whether - now knowing all they know - they really, really want to leave the EU.
At a press conference on Wednesday, Ms Soubry said of the Conservative party: "The battle is over, the other side has won".
Liverpool can 'hurt' Bayern in Munich, says Henderson
The fans were a bit nervous. 'I'm not unhappy with the result, but you always want to get an away goal in the in knockout ties. They braced themselves for the mythical Anfield storm and defended stoutly enough to ensure it never arrived.
"It is time to realign British politics and get back to the centre moderate ground", she said.
"Ending that membership after four decades was never going to be easy".
Work and Pensions Secretary Amber Rudd said it was a "great shame to have lost the commitment and undeniable talent" of the three MPs.
Two Labour MPs, Peter Kyle and Phil Wilson, have taken the lead in building a cross-party coalition to support the proposal and this is making progress.
"I am saddened by this decision - these are people who have given dedicated service to our party over many years, and I thank them for it", she said.
"I guess we now know how their policies and values differ from Labour". The party leader called on them to step down from their positions in Parliament and "put themselves up for election".
How that would translate into seats would depend on where the votes were cast and how many Independent Group MPs were running. "If we don't try, we are surrendering our country and frankly we don't deserve the job that we have".