A third of the Cabinet could walk out if Theresa May steers the country towards a no-deal Brexit, former Conservative Sarah Wollaston claimed amid speculation that more MPs could follow her to the new Independent Group.

Both Labour and the Conservatives are braced for further walkouts as the turbulence at Westminster seems set to continue.

Dr Wollaston claimed the Tory party was “destroying itself” as Mrs May drifted to the right under pressure from the European Research Group of Brexiteers.

The Health Select Committee chairwoman was one of three Conservatives who walked out on Wednesday to join eight ex-Labour MPs in the Independent Group (TIG).

“I know that there are many colleagues on my side who will be watching carefully and expecting Theresa May to be certain that she is not going to take us out on a no-deal Brexit,” Dr Wollaston told BBC Radio 4’s Today programme.

“Certainly I think that a third of the Cabinet, I’m pretty clear, would walk if they were looking at a no-deal Brexit.”

Labour leader Jeremy Corbyn urged the TIG MPs to stand down and fight by-elections under their new banner, which he dismissed as “the failed business-as-usual politics of the past”.

“It is disappointing that some MPs have left our party to sit with disaffected Tory MPs,” he said in a video message released on social media.

“But we cannot return to the failed business-as-usual politics of the past, and it is only Labour that offers solutions to the challenges people face today.”

Responding to the accusations of defecting MPs like Luciana Berger that he had failed to tackle anti-Semitism in Labour ranks, Mr Corbyn said he was “utterly determined to root out anti-Semitism from our party and our country”.

Dr Wollaston said she expected more defections “in the coming week” from both Labour and Tories if Mr Corbyn did not commit to a second referendum and Mrs May failed to rule out a no-deal Brexit.

“If Jeremy Corbyn doesn’t come out for a right to vote, I think very many Labour MPs will realise that the game is up and they will shift, and I think likewise on my side of the House if Theresa May doesn’t take no-deal off the table, more of my colleagues will join us,” she told BBC1’s Breakfast.

Dr Wollaston said “the Tory party has changed, I think it has changed irredeemably”, adding: “I would say the Tory party is destroying itself.”

The Totnes MP joined the new group alongside former minister Anna Soubry and South Cambridgeshire MP Heidi Allen.

Ms Allen said she believed that “a third of the party” – around 100 Tory MPs – shared her frustrations at the direction of the Conservative Party.

Ex-education secretary Justine Greening and former attorney general Dominic Grieve both indicated they would leave the party if the Government backed a no-deal Brexit.

“It is something that I have considered, but I have reached a different conclusion for the moment,” Ms Greening told Today.

“I don’t think I would be able to stay part of a party that was simply a Brexit party that had crashed us out of the European Union,” she said.

As attacks on the Prime Minister from ex-Tory MPs intensified, Ms Soubry accused Mrs 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…  I look at the evidence, and I think she’s got a problem with immigration.”

Responding to Ms Soubry’s comment, Mrs May’s official spokesman said: “The Prime Minister is focused on delivering an immigration system post-Brexit which allows us to take back control of our borders and ensures this country continues to allow in the brightest and best.

“Immigrants make a huge contribution to our public services and economy and that’s going to continue after Brexit.”

POLITICS Labour(PA Graphics)

Ms Soubry said former prime minister David Cameron made a last-ditch bid to try to stop the three Tory defectors quitting.

She told The Times Red Box podcast that Mr Cameron sent them a text saying: “Is it too late to persuade you to stay?”

The Prime Minister has said she was “saddened” by their decision to quit and insisted that under her leadership the Tories were offering “decent, moderate and patriotic politics”.

But the three MPs who quit on Wednesday said they were not contacted by the current leadership before their decision, despite the intervention by Mr Cameron.

And Ms Greening said she had “not seen the Prime Minister recently” despite asking “on multiple occasions”.

Bracknell MP Phillip Lee, who quit as a justice minister over Brexit and was named by Ms Allen as a potential future defector to the TIG, was seen visiting 10 Downing Street on Thursday.

The Right to Vote group, which is chaired by Dr Lee, said he was discussing the campaign’s calls for a pause in the Brexit process and a possible second referendum.

“Talks were open and we are encouraged she listened to our case,” the group said.