British Labour and Conservatives parties 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 program “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 Labor'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 program: 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.
A number of other MPs have expressed sympathy with the group's grievances.
Speaking to the Express Star, Labor's Mr Austin said he would think long and hard about his future in the party.
And Conservative Ms Greening told the Today program 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.
I would certainly cease to take the whip if I thought the Government was about to take us into a No Deal Brexit. I am absolutely clear about that
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.
Tory MP and vice chairman of the ERG Mark Francois denied his group was a party within a party that had taken control, saying they were a group of Conservative MPs who are passionately committed to honoring the democratic decision of the British people that we should leave the EU.
He added: Conversely, Anna, Heidi and Sarah are now a party without a party, who are committed to precisely the opposite. As a result, we shall see how they get on.”
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.