The church of the state

I saw the news today that the name of the new Bishop of Peterborough has been announced. The wording of the press release made me think, though. I know the C of E is the established Church, but it does seem odd that the Prime Minister's Office make the formal announcement. No offence to Peterborough (it's a very nice place), but I would have thought the PM's office have more pressing issues to deal with.