This is honestly a very good question. The US has no official religion, and yet it’s more of a theocracy than the UK in practice. I believe it has more to do with actual practice than anything else. A “pure theocracy” basically says that the monarch is divinely selected. In a way, this used to be the thinking in many parts of the UK, although I don’t believe it has ever been known as a theocracy. The UK now has religious freedom, and as far as I know, there are very few religious laws handed down from the monarchy. So you could argue it’s a theocracy by a literal definition, but not in practice. Being head of the Church of England is primarily a handed-down tradition, with very little power over religion overall.