But for the Conservative Party to overthrow May, several stages need to be completed.
Firstly, to trigger a vote of no confidence, 15% of Tory MPs — 48 in total — must write to Sir Graham Brady, chairman of the Conservative backbench 1922 Committee.
Sir Graham — MP for Altrincham and Sale West — has led the committee since May 2010.
Also known as "The Men in Grey Suits", the '22, is seen as the voice of rank-and-file MPs, representing the mood of the party.
CHALLENGE: Theresa May is facing a possible leadership contest over Brexit (Pic: REUTERS)
ALL SMILES: Negotiations between the UK and EU leaders have been strained (Pic: REUTERS)
CHAIRMAN: Sir Graham Brady MP heads the 1922 Committee (Pic: GETTY)
“The Men in Grey Suits”
Nickname for 1922 Committee
The '22 has an 18-member executive committee with a chairman or chairwoman — usually a senior MP — elected by committee members.
It is named after a meeting of Conservative MPs on October 19, 1922, who ended the party's coalition with David Lloyd George's Liberals and brought down the government.
Losing a no-confidence vote in the 1922 Committee is a massive blow to a Conservative leader.
In October 2003, then-leader Iain Duncan Smith lost a vote by 75 votes to 90 and was promptly dumped by the party.
Even if May wins the votes of more than 50% of the 315 Tory MPs, a close election could still damage her authority.
If she loses the vote, she would not be able to stand in a leadership contest which would then be arranged by Sir Graham.
Leadership candidates must be nominated by two Conservative MPs.
If only one candidate comes forward, they are made leader without an election.
OVERTHROWN: In 1922 a group of Tory MPs who brought down Liberal PM David Lloyd George (Pic: GETTY)
DIVIDED: Anti-Brexit campaigners in London at the weekend (Pic: GETTY)
BETRAYED: Brexit supporters march through the capital (Pic: EPA)
The number of candidates is whittled down to a shortlist of two in a series of votes by MPs.
In a final runoff, the remaining two then go to a postal ballot of all Conservative Party members across the country.
This whole process may take as long as 12 weeks, although many rebel MPs believe it could be completed far quicker.
Read Daily Star Online's handy explainer on how the Brexit Irish border backstop works.