Face of Nation : The former Chancellor said he would not be willing to back a Tory leader pushing a policy that is “totally incompatible with everything the Conservative party has stood for” over decades.
Mr Clarke also made clear that he would be willing to usher in a government led by Jeremy Corbyn in order to thwart a no-deal Brexit.
Conservative leadership frontrunner Boris Johnson on Monday doubled down on his pledge to take Britain out of the European Union on 31 October, insisting he would “not bottle it”.
He has previously made clear that he would be prepared to do so with or without a deal.
But, asked whether he could support a vote of no-confidence in a PM pushing a no-deal, Mr Clarke told the BBC’s The World at One: “If it’s heading for a no-deal simply because the government can’t go round doing anything then, yes, I think I would.”
Pressed on whether he could back a Labour-led bid to bring down the Government, the Tory grandee said: “It depends on the circumstances at the time and [what] whoever is prime minister is putting forward as the policy he is going to pursue.
“But I am not going to vote in favour of a government that says it’s going to pursue policies which are totally incompatible with everything the Conservative party has stood for under all those prime ministers for the decades that I’ve been in parliament.”
Mr Clarke’s comments came as Defence Minister Tobias Ellwood said a string of Tory colleagues would be willing to back a vote of no confidence in the next Conservative leader if they tried to take Britain out of the EU without an agreement.
Speaking to the BBC’s Panorama, Mr Ellwood said: “I think a dozen or so members of Parliament would be on our side, would be voting against supporting a no-deal, and that would include ministers as well as backbenchers.”
The Government’s slim Commons majority means that a rebellion of that size is likely to bring it down – and could force the next Prime Minister to hold a general election.
Asked whether Tories opposed to a no-deal Brexit had the “numbers” to bring down the Government, Mr Ellwood said: “I believe that absolutely is the case.“
Labour has already signaled that it could try to force a vote of no confidence in the next Prime Minister as soon as they take up post, and Shadow Chancellor John McDonnell on Monday said his party’s “door is always open” to Conservative MPs mulling a no-confidence move.
But prisons minister Robert Buckland downplayed Mr Ellwood’s “premature” claims that Tory MPs would be willing to pull the plug on their own Government to halt a no-deal.
“I think this is wild talk, frankly,” he told the BBC’s Politics Live.
“Anybody who can predict precisely where we are going to be at the end of October is a better politician than I am.
“And I think making that sort of threat now is frankly premature. Let’s look at the consequences of it.
“The consequences could be to usher in a Corbyn-SNP coalition. Is any self-respecting Conservative going to want to be complicit in that? I don’t think so.”
The row came as The Sun reported that the new Conservative leader will be announced on 23 July before taking up post on 24 July, after Theresa May holds her final session of Prime Minister’s questions
Mrs May’s exact departure plans are still being finalised, but a senior Conservative source told the paper: “Everything is pretty much in place.
“We’ll have a new leader on Tuesday July 23, and a new PM by the end of Wednesday afternoon, as long as Theresa is amenable to that, and nobody thinks she won’t be.”
