Ex-Tory MP Sarah Wollaston suggested that the Conservative party was "destroying itself" amid speculation former colleagues could follow her to the new Independent Group.
"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," she 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."
Read more: Sarah Wollaston, Heidi Allen and Anna Soubry quit Conservative Party for Independent Group
Dr Wollaston said "the Tory party has changed, I think it has changed irredeemably", adding: "I would say the Tory party is destroying itself."
Former education secretary Justine Greening said she was staying in the Conservative Party "for the moment".
Ms Greening warned that the Tories would no longer be credible if they simply became "a Brexit party".
The ex-Cabinet minister, who has focused on improving social mobility since leaving office, said: "Right now, I have to say, I don't think I see enough ambition in the party that matches mine on this agenda."
Read more: In full: Resignation letter of Anna Soubry, Sarah Wollaston and Heidi Allen
Asked if she would follow her three former colleagues to the Independent Group she told BBC Radio 4's Today: "It is something that I have considered, but I have reached a different conclusion for the moment."
But she indicated that if the Tories were taking the country towards a no-deal Brexit she would leave.
"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.
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