When ol' Lizzie died, the Archbishop of Canterbury let us all know that God dropped him a message to say the King Charles should succeed to the throne, which worked out awfully lucky with what was already being planned. The Head of State of the United Kingdom is claiming to derive their authority from God (aka Divine Right of Kings), state and church are officially unified and clerics are a required part of the legislature, does that not make it a Theocracy by any reasonable definition?
I think this is where you get into de facto and de jure arguments. The UK is a de jure theocracy, sure. But the reality is that the Church of England specifically - and religion more generally - afaik doesn't seem to have any real political power. It seems like capital doesn't really need them to help wield political power.
Now in the US, I'd argue it's the opposite: separation of church and state on paper but in many ways it is a de facto theocracy. The religious - white evangelicals in particular - have tremendous soft power as well as social power in a lot of places (try having much of a social life outside of church in the south outside of Atlanta, for example). Of course, this is because the religious in the US are particularly valuable to capital.
So sure, the UK may be a "theocracy" on paper but I don't think it means much.
For sure, all of this is entirely agreed, just looking at the technical observations.