It doesn't work quite like that.
They get him to resign, usually via a vote of no confidence. Then people choose from the different MPs that put their names forward.
There are two who have been making their ambitions known: the chancellor of the exchequer, Rishi Sunak, and the foreign secretary, Liz Truss. They are his number 2 and number 3.
Personally, I'd rather stick with Boris, flawed as he is. He's got the big things done. But people are clearly very angry that he was casual about the rules.
On the other hand, does it matter that Churchill was a drunk if he also won the war? I think Boris has got the big things right even if he seems simply unable to obey rules.