Labour and the Conservatives could face more resignations, with members of the new Independent Group saying they expect more MPs to join them.
Ex-Tory MP Heidi Allen told ITV’s Peston programme “a third” of Tory MPs were fed up with the party’s direction.
Tory MP Justine Greening said she would quit her party if it allowed a no-deal Brexit, while Labour’s Ian Austin said he was considering his position.
MPs from the new group say they stand for “the centre ground of politics”.
The group was set up by eight defecting Labour MPs unhappy about their party’s handling of Brexit and anti-Semitism.
They were later joined by three pro-Remain Tories – who accuse the Conservative leadership of allowing right-wing hardliners to shape the party’s approach to Brexit and other matters.
Chancellor Philip Hammond said he was “saddened” by his former colleagues’ comments, but denied the “relatively small hardcore” – namely the pro-Leave European Research Group – had taken over.
He told BBC Radio 4’s Today programme: “The Conservative Party is, always has been and, in my view, must remain a very broad church.
“I understand their concerns, but I hope over time they will feel able to rejoin the party and help maintain that.”
‘Off the rails’
A number of other MPs have expressed sympathy with the group’s grievances.
Speaking to the Express and Star, Labour’s Mr Austin said he would think “long and hard” about his future in the party.
And Conservative Ms Greening told the Today programme she would find it hard to stay in a party that “crashed us out of the EU”.
The former education secretary said: “I am not prepared to be part of a Conservative Party that blithely thinks that’s some kind of strategy for Britain in any way, shape or form.”
Sarah Wollaston, one of the MPs who left the Conservatives for the Independent Group, estimated that one third of the cabinet would quit if the UK left the EU without a deal.
Mr Hammond would not reveal if he would resign his post, but he said the fact a no-deal Brexit was “always a possibility” had “focused minds” and was encouraging compromise.
However, he added that the government was “absolutely committed to avoiding [a no-deal] outcome and making sure that we get the deal”.
Meanwhile, former Attorney General Dominic Grieve told BBC’s Newsnight he admired the courage of the 11 members of the Independent Group and agreed totally with their support for another EU referendum.
He said he would not be able to stay in the Conservative Party if it “went completely off the rails” and backed leaving the EU without a negotiated agreement.
Conservative defectors insist ‘no way back’
Prime Minister Theresa May has rejected claims the party has abandoned the centre ground in its pursuit of a hard Brexit, pledging to continue to offer the “decent, moderate and patriotic politics that I believe the people of the UK deserve”.
And senior Conservatives have suggested the door is open for the three Tories who quit – Ms Soubry, Ms Allen and Dr Wollaston – to return one day.
But Ms Soubry insisted there was no “going back” because the soul of the party had been overwhelmed by a rightwing “purple Momentum”.
She also revealed that former PM David Cameron had made a last-ditch attempt to stop the trio from quitting.
Speaking to The Times Red Box podcast, she said Mr Cameron had sent them a text saying: “Is it too late to persuade you to stay?”
Ms Allen also said she could not imagine returning “because if we do our jobs right there won’t be a Tory party to go back to”.
She said she was “hopeful” that what she described as “good, sensible centre ground colleagues” would join the new group.
Corbyn wants defectors to quit
Meanwhile, in a video released on Twitter on Wednesday night, Labour leader Mr Corbyn said defecting MPs should resign and put themselves up for election.
He said this would be the “democratic thing to do” because they wanted to “abandon the policies on which they were elected”.
While the Labour leader said he was disappointed, he suggested the eight were replaceable and the Labour movement was “greater than the sum of its parts”.
Other Labour MPs have said they will consider their futures unless Mr Corbyn listens to their concerns about the culture of the party and acts on them.
Momentum, the Labour movement backing Mr Corbyn, is to hold “mass canvassing events” in several constituencies to build support in the event of any by-elections.
It says it will build support in Streatham, Stockport, and Penistone and Stocksbridge – the constituencies of Chuka Umunna, Ann Coffey and Angela Smith respectively – in the next few weeks.
Labour apology over anti-Semitism
Mr Corbyn has said he will not change Labour’s direction in response to the defections but has repeated that tackling anti-Semitism is a priority.
He has been accused by departing MPs, including Joan Ryan and Luciana Berger, of allowing a culture of “anti-Jewish racism” to flourish and for Jews to be “abused with impunity” by his supporters.
One of Mr Corbyn’s senior team, Barry Gardiner, apologised to the Jewish community in the House of Commons on Wednesday, saying it had “let them down”.
Mr Corbyn said he recognised the party had work to do to restore trust among the Jewish community, and needed to persuade people the party was its “ally” in the fight against anti-Semitism.
The party said it had suspended the membership application of left-wing firebrand Derek Hatton over Twitter comments he made about Israel in 2012.