The use and reuse of "nick" is pretty much normal here. The use of the word to describe both the police station and the cells isn't two different meanings, however, it's just a general term for both. You could say that "Jim got nicked by the Old Bill and charged down at the nick before they banged him up in the cells". But you couldn't say "Jim got nicked by the Old Bill and was charged at the nick and then banged up in the nick".