Wasn't nicked also being arrested by the Bill?
Yes, though if someone said, "I was nicked by the Old Bill and banged up" instead of, "I was arrested by the police and jailed" it would sound very Cockney (East End of London) to my ears, though it's possible people in other areas of England would say that too. If you were in Scotland you'd say. "I was lifted by the polis and put away" instead.

