What is the current procedure under Conservative Party rules for kicking out a leader who doesn't want to go?
British political parties, at least the major ones, are historically not very tolerant of a leader who blows an election as May did this one.
The leader in these cases often resigns or possibly faces a back bench revolt.
Yeah, but what is the actual mechanism? In Australia, not too long ago, the caucus of either major party in Parliament could move to hold a leadership election at any time, and just vote in a new leader in one day, so a coup could happen pretty much instantly. This is no longer the case for the Labor Party, so a coup would now be a more drawn out, bloody affair, and it's harder to get rid of a struggling leader.
What about the UK? IIRC, in Thatcher's day it was pretty easy, but now it's become more complicated, because the wider membership of the party is involved as well?