I think that lack of urbanization in any place has the opposite effect, religion always had a firmer hold in rural areas. In both countries (really, all over the world), progressing urbanization usually goes hand in hand with decline of religion.
As for CofE, it is, for all intents and purposes, Catholic Church with the Queen as the Pope. Bureaucracy might be less extensive, but from what I've seen of it, it's just as stiff as the Catholic Church. Soon it might be even more, considering the new Catholic Pope. The head of CofE doesn't look like she's going to quit anytime soon.