The former Attorney General, Dominic Grieve — a staunch remainer — told the BBC's Radio Four that "twelve or more" high-ranking ministers are on the cusp of walking away from Miss May's cabinet if she does not extend the Brexit negotiations with the EU beyond the March 29 deadline to avoid a no-deal Brexit.
If May does not acquiesce, then it is possible that those MPs will leave by 27 February — the next round of voting on Brexit motions — to begin actively protesting against the no-deal possibility.
When asked by one of the show's presenters whether such resignation en masse could topple May's increasingly shaky government, Mr Grieve replied that,"yes it could and this isn't a desirable outcome."
"The irony of all this is that most of us in the Conservative party are sufficiently united to want to try to operate a coherent government. But the truth is we're finding it harder and harder to do. It started to bring into question whether in fact the government is able to operate in the national interest," he added.
Mr Grieve said that the MPs have lined up to express their anxieties to Prime Minister May in order to "express their concern that if by the end of February there is no deal that has been got through the Commons, we ought to extend."
READ MORE: We Will Not be Leaving the EU, Brexit Will Never be Delivered
"If the Prime Minister refuses to do that, I think they face a very difficult choice, because unless we as a Parliament and as the House of Commons start to work together to take the necessary steps to prevent no-deal happening, no-deal could just occur. It could all be so chaotic, it might just happen by accident. My view is that if they feel she is not taking those steps, I think they are going to have to resign," he added.
The development comes the day after Miss May endured yet another humiliating defeat over her Brexit plans in parliament. MPs voted by 303 to 258 — striking a majority of 45 — against a bill supporting the government's negotiating strategy to extend the March 29 deadline for at least three months.
READ MORE: UK Lawmakers Reject Amendment Calling on Gov't to Delay Brexit
The sting of defeat was stronger this time around as it was partly facilitated by many within her own party who're members of the pro-Brexit European Research Group (ERG). Ministers in that group argue that miss May's strategy is essentially too soft, demanding a guaranteed clean break from all EU institutions such as the customs union and a hard end-date for the Irish backstop.
Conservative Business minister, Richard Harrington, accused the ERG, led by Jacob Rees-Mogg, of "treachery" and said they were "not Conservatives."
"The Prime Minister has done a pretty good job of standing up to them up till now, but they were drinking champagne to celebrate her losing her deal and I regard that as being treachery," Mr Harrington is widely quoted as saying.