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'd say that you can use the Confessional State label without any sort of controversy, while the label Theocracy would have to be part of a broader critique. From what I understand the british House of Lords doesn't have the power to veto anything that the Commons do. And however Divine is the Right of Kings, stuff like Royal Assent subsists due to the rights of a head landlord rather than that of a head preacher. Case in point if I'm not mistaken the Queen's use of Assent was in respects to laws affecting her estate rather than religious law.
When people say Theocracy they mean old Tibet, Iran or Vatican City. Imagination goes straight to priesthoods which serve in some way as the bureaucratic apparatus of the state. I'm not British, but to what extent does the influence of something like the lords spiritual and the Church of England exists due to a cultural cachet, economic levers, or social status rather than hard constitutional power?