>The UK has no constitutional method to remove a PM. I not sure this is correct, a vote of confidence in Parliament. Will bring down the government. Hence the PM.
Parliament can also impeach ministers. It hasn't bothered trying for about 180 years because a vote of no confidence is simpler, but it hasn't given up the power (and it's hard to argue that it's somehow fallen into abeyance through lack of use, as there's precedent for a gap of a couple of centuries between impeachments).
But that doesn't bring down the PM personally.
The last VONC to pass was in 1979, and Callaghan continued to lead Labour (albeit to defeat) in the General Election.