well in UK you don’t vote for the PM. you vote for your local representative (Member of Parliament, MP). whichever party has the most MP becomes the ruling party and forms government, and the leader of that party becomes PM. if members of that party lost confidence in their leader, they can choose a new one. so if someone wants to be the new PM, they can do that by getting MPs behind him.
formally the new PM must be chosen through a leadership challenge process, but if the current PM sees the writing on the wall, they might choose to just resign with some dignity intact, instead of being dragged out kicking and screaming.
well in UK you don’t vote for the PM. you vote for your local representative (Member of Parliament, MP). whichever party has the most MP becomes the ruling party and forms government, and the leader of that party becomes PM. if members of that party lost confidence in their leader, they can choose a new one. so if someone wants to be the new PM, they can do that by getting MPs behind him.
formally the new PM must be chosen through a leadership challenge process, but if the current PM sees the writing on the wall, they might choose to just resign with some dignity intact, instead of being dragged out kicking and screaming.
Think of it like the speaker of the house (assuming the one asking for clarification is American). They just have more than two parties.