I think that's quite complicated, while Britain is mainly supposed to be secular I think it the church still has a lot of influence within the government. For one thing, the Queen is still considered the head of the Church of England, and Bishops and Archbishops still sit in the House of Lords.
Good place to start may be Wikipedia Church of England
We still get religious programming on the BBC, faiths apart from Christianity are now more represented than they used to be.
I don't think we get the same issues as the US regarding the separation of church and state as the church of england (and most of churches of europe I think) take a more modern viewpoint on life than the fundamentalists that seem so prevalent within American politics. This is just my view though, so I'm not going to be providing you with any examples.