It could be far more so. Anglicanism is the official state religion of England but it has minimal effect. The monarch does not rule and the handful of clerics in Parliament comprise about 3% of the House of Lords, which can only delay bills and only if the government lets them. So they're a tiny minority in an organisation which collectively has only minimal power.
Anglicanism is not really a state religion at all despite being dressed up as one. It's the decorative remnants of one, retained for tradition. The idea that it's so powerful that the only way it could become more so is if the UK became a full blown theocracy is silly.
Perhaps I should rephrase. I wasn't referring to the actual powers of the Church of England or attempting to suggest that it is already so powerful that the only way it could be more so would be for the UK to become a theocracy - that would indeed be a bit ridiculous. Rather, in response to the claim that "There is no state religion" I was postulating that it is still about as official as you can get. If anyone is interested perhaps they could do the research to find out how many other countries have the same level of official links between church, head of state and parliament.