I'm not at all religious but I love the smell of Orthodox Churches and feel really humbled amongst all the history they exude. We owe a continuity to the Church tradition as far back as the early Hellenic gods. It revolves more around the recording of our heritage than directly influencing it. It certainly does not affect our politics since we have a strong political (democratic) tradition which is just as powerful but independent.
I think people from other religions cannot comprehend how we manage with the richness both of our political life, and also our "larger than life" religious heritage; yet still manage to keep them separate.
The Church of England is more influential in the politics in the UK (as well as in the House of Lords) than the GO religion is in Cyprus / Greece.
Look how much Tony Blair had to
hide the fact he was Roman Catholic (because we all know the RCs and CoE have been bitter enemies since Henry VIII's time
).