There are plenty of taxes that only some people have to pay, for example, the fee to register a car.
> Furthermore the state isn't in charge of administering it anyway, it's a civil matter brought about by the BBC (or rather the company which is subcontracted to enforce licencing). The BBC has the authority to do this based on the Royal Charter that governs it
I'm trouble understanding how this doesn't make it part of the state? It is a 100% state-owned entity to which the state has granted (in a "Royal Charter") the ability to collect taxes... the distinction you're trying to draw seems meaningless to me.
Sure there may be two separate entities, one called "The UK Government" and one called "The BBC" where neither is part of the other, but structurally I don't see how you can claim that they're not both part of "the State" in general.