I’ve read the Queen (or King, if there was one) has some sort of Constitutional veto power, and maybe more, but the royals very rarely use it. The PM thing, as far as I understand, and I’m probably wrong, is that which ever party has the ruling majority (and there about 7 parties I think), gets the head of their party as PM, or that party picks the PM.
Or something.
So far it seems to suck mightily. The last bunch of PMs are the proof.
THinking on it a little more, it seems like the Cabinet Ministers share the executive power with the Prime Minister and the PM is something like first among equals. It is certainly easier to get one you don’t like out of there!