But after stopping, a thought flashes across your mind: what if they're not a real officer? You have no idea what his intentions are or what he might want.
This actually happened for real last year, where a woman was followed by a silver Vauxhall which had a flashing blue light on the dashboard.
When she stopped, she realised the man was wearing a hooded top and was not a genuine officer.
So what can you do to ensure a stop by an unmarked car is genuine?
What should I do if I suspect the police car pursuing me is fake?
Call 999. Officers will be able to check a number plate and description of any car to work out if it's a genuine officer or not.
The advice from police is that if you're unsure whether the car is genuine, do not stop. Drive to the nearest police station or public place like a petrol station.
In remote areas, the driveway of an occupied house could work if you're desperate. But definitely do not stop anywhere secluded.
Does an unmarked police car have the power to pull me over?
Yes - but the officer must be wearing uniform in order to carry out the stop. If they aren't wearing uniform, they shouldn't be pulling you over.
Do the police need a reason to pull me over?
No, the police have the power to stop any vehicle and ask for your name, date of birth and to see your driving licence and insurance and MOT documents. These can usually be produced later at a police station.
A genuine police officer should also be carrying a warrant card.
Even if you decide not to stop straight away, it is advisable to signal that you have acknowledged the request, in case it is a genuine officer.
Do not drive off at speed, making it seem like you are trying to get away.
What about when I have stopped?
Keep the doors locked until you are sure it is the police. Have your mobile to hand in case.
You can ask to see a warrant card, which should carry the police officer's name and photograph, through the closed window and locked door.