It's not really registering with the police, though they probably get access to the information. When you do it you go to the council building and register there (at least when I last did it several years ago), so it's more like registering with the city. This means that things like local taxes and such go to you automatically. I do know a lot of people who aren't registered where they live, because they're illegally subletting or something so they're registered at their parents' place or whatever. It's pretty accepted that this is common.