What is a vote of no confidence?
The Conservative leadership contenders have been warned that around a dozen Tory MPs might support a vote of no confidence in the government to prevent a no-deal Brexit.
Boris Johnson - the frontrunner ahead of Jeremy Hunt - says the UK must leave the EU by 31 October, come what may.
But what would such a vote of no confidence actually mean?
What is a no confidence vote?
It is a chance for MPs to hold a vote on whether they want the government to continue - and it has the power to trigger a general election.
Any MP can propose a motion of no confidence, but that doesn't mean it would be debated.
However, if the leader of the opposition introduces the motion, convention means the government will provide time for a debate to take place.
The wording of a no confidence motion is: "That this House has no confidence in Her Majesty's Government."
What happens if the government loses?
Losing a no confidence vote starts a critical 14-day period, after which a general election could be triggered.
To prevent that, the existing government - or an alternative one formed during that period - must persuade MPs to pass a vote of confidence.
The wording of the confidence motion has to be: "That this House has confidence in Her Majesty's Government."
The date for the election, if a confidence motion isn't passed, would be 25 working days after Parliament is dissolved.
There are no firm rules about who, if anyone, should get the chance to form an alternative government during the 14-day period. The leader of the opposition is clearly a likely candidate, but that is not an inevitable outcome.
The Cabinet Manual - a document which sets out the main rules covering the working of government - suggests that the principles applied should be similar to those after an election in which no one party wins a majority.
That means that the old prime minister should only resign if and when it's clear that somebody is more likely to have the support of MPs.
So it's possible that the existing prime minister would stay in place, or that more than one leader would get a chance.
How could the next Tory prime minister be defeated?
Whoever wins the Conservative Party leadership election is expected to become prime minister.
But they will lead a government with a very small majority.
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Since the 2017 general election the Tories have been reliant on the 10 DUP MPs in the House of Commons. And their majority has become narrower over time after a series of defections.
So, if some Tories are prepared to vote against them in a no confidence vote the new prime minister could be in office for only a brief period.
Previous no confidence votes
Before the law was changed in 2011 to say elections would be held every five years, the rules governing votes of no confidence were different.
Prime ministers had the power to call general elections whenever they wanted. That meant they could turn votes on particular bits of legislation into "confidence votes".
In other words they would threaten to call an election unless MPs backed a new law.
However, this is no longer an option. Elections are only triggered by no confidence votes with precisely the right wording.
However, the fundamental principle remains the same. Governments can only continue if they have the confidence of the House of Commons.
There's only been one occasion since World War Two when the government lost a no confidence vote.
That was in 1979, when the Labour minority government fell and was replaced by Margaret Thatcher's Conservatives at the general election which followed.