> In the UK you very much vote for a person
We're talking about the PM here. You vote for a person who then votes on the PM, so it's an indirect system.
> using the arcane first past the post system.
FPTP sucks, but I've never heard it called arcane before. It's arguably the default normal way to vote for anything.
In the UK you very much vote for a person, using the arcane first past the post system. People usually vote based on party allegiance, but at the circonscription level you cast a vote for the one winner, resulting in massive disenfranchisement.