Both Labour and the Conservatives are braced for further walkouts as the creation of a new independent grouping of MPs continues to rip through the political landscape.
Tory former attorney general Dominic Grieve said he would leave the party if the Government backed a no-deal Brexit.
ITV News Political Correspondent Paul Brand said it was clear former minister Justine Greening would also quit on that basis.
Speaking to ITV News in Brussels, Labour party leader Jeremy Corbyn spoke of his "regret" after eight Labour MPs quit the party on Monday. He added it was "entirely logical" the eight should resign and if they wish to stand again there should be a by-election.
Deputy Labour leader Tom Watson described the party's response to the defectors as a "knee-jerk" and "spiteful" reaction.
When asked about Mr Watson's comments the Labour leader told ITV News his raised the need for by-elections as a "democratic argument".
He said: "I don't behave in a knee-jerk or spiteful way, I simply say if you've been elected to Parliament on a manifesto for the many not the few, which you were in the General Election and you then resign from the party and say you're doing something else because you're an individual who happens to be an MP.
"Surely you owe something to the people that put you there?"
He added: "If you resign, have a by-election and decide whether you or somebody else will be the MP for that area. Surely that's democratic?"
When asked if he would welcome the defectors back if they ever wished to rejoin the party, Mr Corbyn seemed unsure.
He said: "If they apply to come back in the future, obviously we can look at it."
When asked about the timing around when the now suspended Derek Hatton was allowed back into the Labour party Mr Corbyn said it was "coincidence".
The former deputy leader of Liverpool council was suspended just two days after being allowed back in to the Labour party following his expulsion 34 years ago.
The suspension is believed to have followed concerns being raised about Mr Hatton's Twitter history.
The Conservative party have also had its share of defectors who have criticised the Government's handling of Brexit.
Chancellor Philip Hammond said "everything he does" is to ensure "we avoid a no-deal Brexit".
He said: "I've always been very clear that no-deal would be a very bad outcome for this country, so everything I do everyday is designed around ensuring that we avoid no-deal and the way to avoid no-deal is to get the deal that we have negotiated through parliament.
"We recognise that means we have to address the concerns that parliamentarians have raised and that is exactly what we are doing at the moment. That is what this process is about," he added
TIG MP Heidi Allen said that around 100 of her former colleagues on the Tory benches shared her frustrations at the direction of the Conservative Party.
Ms Allen told ITV’s Peston: “I’d say a third of the party.”
Lord Peter Mandelson also said he felt “morally compromised” staying in Labour following anti-Semitic abuse endured by people such as ex-Labour MP Luciana Berger.
The Labour peer told ITV’s Peston: “When I look at the sort of anti-Semitic abuse to which Luciana Berger has been subjected, but not alone, many others in the party, I feel ashamed, I feel actually quite morally compromised staying in a party that can spew out so much hatred towards other members of their own party.
“Now what is Jeremy Corbyn going to do about this? I mean, this risks growing from a splinter into a cavernous split in our party if he doesn’t take action to stop it.”
Lord Mandelson urged Labour MPs to remain in the party.
The defections of Ms Soubry, Ms Allen and Sarah Wollaston from the Tories took the number of TIG MPs to 11.
High-profile ex-minister Anna Soubry said Mr Cameron had reached out to the MPs as they prepared to turn their backs on the Tories for TIG.
Ms Soubry told The Times Red Box podcast that Mr Cameron sent them a text saying: “Is it too late to persuade you to stay?”
The chancellor has also told ITV News he hopes the three former Tory MPs will rejoin the "Conservative family".
He said he was "very saddened" that the three MPs left the Tory party, before adding, "I very much hope that in time they feel able to come back into the Conservative family."
As attacks on the Prime Minister from ex-Tory MPs intensified, Ms Soubry accused Theresa May of having a personal “problem” with immigration.
Ms Soubry told BBC2’s Newsnight: “The only reason why she will not agree to the single market is because of free movement of people.
“And I think what’s really worried me about Theresa, and she has history in the Home Office that supports this, because I’m an old barrister, I look at the evidence, and I think she’s got a problem with immigration.
“I really, honestly do.”
Asked if she meant it was a personal rather than policy issue for the PM, Ms Soubry said: “Oh yeah, I think she has a thing about immigration and I don’t know where the hell that’s come from.
“Because in a modern Conservative Party, when you again look at the evidence, you know, if we don’t have all these people that come and do all this work in our country, who on earth is going to do it?”
Tory former attorney general Mr Grieve told the BBC: “I can’t predict where I might be if the party goes completely off the rails – that’s another matter.”
He added: “The Government which I am supporting implementing a no-deal Brexit – what would I do?
“I would not be able to maintain my support of the Government.
“I would have to leave the party.”