It’s been a rough few days for Theresa May. Things seemed to be looking up for her after the Cabinet agreed to support her Brexit strategy following a marathon meeting at Chequers, but her triumph was short lived. Within seventy-two hours, both the Brexit Secretary and the Foreign Secretary had resigned, leading to speculation that Conservative MPs could soon trigger a vote of no confidence in May’s leadership of the Conservative Party. However, some commentators don’t seem to realize that this is not the same as a motion of no confidence in the Government.
In contemporary British politics, the leader of the dominant party in the House of Commons becomes Prime Minister, but the question of who is to be leader is an internal party matter. Neither the Commons as a whole nor the electorate have any say on the subject. Consequently, any attempt to unseat May as Leader of the Conservative Party would be handled within the Conservative Party, according to the Conservative Party’s rules. If she lost the confidence of her MPs, the party would elect a new leader, who would then become Prime Minister. An early General Election would not be necessary, and the new Prime Minister could theoretically soldier on until the next scheduled poll in 2022.
A motion of no confidence in the Government, on the other hand, is a matter for the House of Commons as a whole. Since 2011, the practice has been regulated by the Fixed-term Parliaments Act. If MPs support a motion of no confidence in the Government, the parties would have fourteen days to try to form a new administration that could maintain the confidence of the House. If that didn’t happen, Parliament would be dissolved and there would be an early General Election.
Despite May’s woes, even ardent Brexiteers should probably think twice before triggering a confidence vote. A typical leadership election takes time (the 2016 Conservative leadership contest was supposed to run from June 30 to September 9), and having one now would make it incredibly difficult for the United Kingdom to agree to a Brexit deal with the European Union before the October deadline. While the last Conservative leadership election was truncated after every candidate except Theresa May dropped out of the race, it’s not clear that a consensus candidate could emerge today given the state of the party. A new Prime Minister would also come under incredible pressure to call an early General Election. As Theresa May knows all too well, elections can have unpredictable results. So while Brexiteers may not like her, letting May stay in place might well be their least-bad option.
 Under the Party’s rules, a motion of no confidence must be backed by fifteen percent of Conservative MPs before it can be put to a vote. If that happens, the entire body of Conservative MPs would decide whether May stays or goes. If the vote went against her, there would then be a contest to find her successor. Conservative MPs would have to decide on two candidates to present to the full body of Conservative Party members, who would then make the final decision.
 To ensure continuity of government, May would likely remain in office until her successor had been chosen.
EDIT: Corrected a misstatement of the Fixed-term Parliaments Act 2011.