Had the same kind of problem one night in Edinburgh!
Just picked up the ex from her work,sitting at a set of lights and an unmarked CID comes round the corner staring at us.I started laughing and then drove away.Next thing i know they are right on my case flashing the headlights at me and waving to the side of the road,well there was no sign of any badges and no blue flashing lights therefore i just kept driving.
Went round several roundabouts more than once and also done several lane cutting exercises at the last minute (to my amusement)
Thought that i had lost them a couple of times only for them to re-appear out some dodgy street!
After about half an hour of this the next thing i know there are 2 panda cars and a van behing me.Blue lights and a pull were the next thing to happen with a load of abuse from the CID!Arseholes!
Was a good laugh though!