You obviously don't live in Suffolk, PSB ;-)
Suffolk police keep a minimum of 2 unmarked vehicles operating on the A14, between Newmarket and Felixstowe, 24 hours per day. Additionally, they're widely used throughout the rest of the county. These vehicles only become noticeable when they turn on their sirens and their well-hidden blue lights. Anyone who regularly drives on main roads around here will encounter these vehicles, with their lights on and sirens sounding, several times a week.
As well as the unmarked traffic vehicles, we sometimes see other unmarked cars (often with plain clothes police in them) on an emergency call. The difference is that these vehicles have a magnetically mounted blue light stuck on the top of them, rather than the built-in lights of the traffic vehicles.
As Ethel says, senior officers from the other emergency services may also have magnetically-mounted blue lights to attach to the tops of their vehicles. Doctors cars can also have emergency lights but the regulations prohibit them from using blue lights. They have to be green.
Chris