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?
This is like how the UK isn't really a monarchy because the monarch rarely exercises their near absolute power. Strangely, the degree of nuance afforded to the arrangement of power in the UK is not only not afforded to many other countries, but their actual nuanced distribution of powers is outright ignored in favor of calling them absolutist dictatorships.
I wanted to gulag my comparative politics professor multiple times.