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Sir John Major, the former Conservative Prime Minister, has threatened to use the courts to try to stop the next prime minister from shutting down Parliament in order to force through a no-deal Brexit.
Most MPs are against leaving the EU without a deal and could try to stop it from happening.
The new prime minister could try to get round this by closing Parliament in the run-up to Brexit day, which is currently scheduled to be 31 October.
Boris Johnson - who wants to succeed Theresa May as Conservative leader and prime minister - has repeatedly refused to rule out such a move.
So how could it work?
How is Parliament normally closed?
The official term for shutting down Parliament is "proroguing" and it normally happens once a year for a short period - usually in April or May.
During this time, all business stops, so most laws that haven't completed their passage through Parliament die a death (although some may be "carried over" to the next session).
MPs keep their seats and ministers remain in position - but no debates and votes are held in Parliament.
This is different to "dissolving" Parliament - where all MPs give up their seats to campaign in a general election.
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So could a prime minister force Parliament to close?
In theory, yes.
MPs do not vote to prorogue, it's a power that rests with the Queen - done on the advice of the prime minister.
So a prime minister determined to force a no-deal Brexit could, in theory, ask the Queen to shut Parliament to dramatically reduce the influence of MPs.
With Parliament not sitting, MPs would not be able to block a no-deal Brexit - for example, by holding of a vote of no confidence in the prime minister.
Jeremy Hunt, one of the leadership candidates, has categorically ruled out proroguing Parliament.
But, Boris Johnson, on the other hand, says he would "not take anything off the table".
GETTY IMAGESWhy would it be controversial?
It would bring the Queen right into the heart of the Brexit dispute.
Normally, a prime minister's request to the Queen to prorogue is extremely straightforward.
In fact, the House of Commons Library says it has been a formality in the UK for more than a century.
But in the current climate, the Queen would have to decide to accept or deny the request.
CHRIS JACKSON
If it was granted, planning for a no-deal Brexit would be much harder.
That's because the prime minister - without a sitting Parliament - would not be able pass laws to cushion the impact of no deal - for example, allocating extra money or resources.
Supporters, however, say such a move would respect the 2016 referendum by guaranteeing the UK leaves the EU on 31 October.
But opponents say it would be undemocratic and undermine MPs - most of whom are against no deal. Amber Rudd, the Work and Pensions Secretary, has called the suggestion "outrageous".
According to the Institute for Government think tank, the last time Parliament was closed to get round opposition to government policy was in 1948 - following the Lords' opposition to the Parliament Bill.
Could it be stopped?
Sir John Major believes the Queen would have to agree to close Parliament if requested - because refusing would create a constitutional controversy.
He told BBC News: "The Queen's decision cannot be challenged in law but the prime minister's advice to the Queen can, I believe, be challenged in law - and I for one would be prepared to seek judicial review to prevent Parliament being bypassed."
While some believe a legal challenge could work, a source close to Boris Johnson told BBC News the threat of court action was "absurd".
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