@Drago or others will correct me, but I thought the police had to have a reason for pulling you over? A light out, or speeding etc. They couldn't just pull you over to check you were road legal.
They can pull you at any time simply to inspect your documents, but it is preferred to have a reason to do the stop. Courts don't like fishing trips and your reason for 'randomly' stopping someone might be called into question if you spot a kg of cocaine on the passenger seat (ie, it may be implied that you've been unlawfully targetting someone without a RIPA). So, if its reasonably possibly they would rather you had a brake light out, broke the speed limit by 1 MPH, weren't wearing a seatbelt etc before stopping you, that that's preference, not regulation.
I only stopped someone cold once when demonstrating the process to a student officer, and lo and behold they had no insurance! 100% strike rate!