[GoLightly]

Having an offical state church was common in all European monarchies at some point. England stopped being an absolute monarchy, so the "ruler" no longer has absolute rule there. I would argue that it stopped being a "theocracy" with regicide.

[Frumious Bandersnatch]

It could also be argued that England is no longer a monarchy and hasn't been since Prince Albert, since the only power that the Kings and Queens of England currently have is prestige (which the royals seem to be determined to squander as fast as they can).

However, from a technical sense, they are a theocracy since the titular head of state is also the titular head of church.