Actually Parliment made them in 1701.
Well, Parliament did change the rules slightly, yes. Even so, though, that Parliament was hardly representative of the people as a whole (only a few percent could vote), and Parliament's power was given to it by the king in the first place (and that came about as a result of several wars where the monarch lost), so even Parliament formally-speaking only gets legitimacy because the monarch says it has legitimacy.
And William the Conquer's direct line is dead, I think.
Well, his direct male line certainly is, but I think that the current monarch can be directly traced back to him through female descendants.
Well, yes, but only in so far as you consider his rule legitimate, and I can't see any fundamental reason (aside from "because I have the biggest stick") why it should be.
This seems to be the best reason. I think that having biggest stick is a pretty convincing reason to have authority.
Sure, but that's basically what I was arguing in the first place. Axe Cop can say "I'm a Cop" because he's strong enough to back it up, and he considers it his duty to enforce the law of the land whether or not he is officially recognised as a police officer.