I, and my driver, are stopped fairly regularly whilst we are driving at night by the police. This is because I am a nighttime escort, and random checks on cars are made routinely after sundown; meaning we get stopped a lot more than your average traveller.
I am always honest about working as an independent escort when asked by the police. They do ask my real name and home address, which I am happy to give them. However I have never been questioned any further than this, and have never, ever been told by the police that it is illegal to have a driver - because it isn't. I also have never had my bag checked, or had the car checked; I don't believe they could do this because they have no suspicion of an offence taking place.
I work in London and around Gatwick as well so I have direct experience of dealing with these particular (and in my experience very professional and knowledgeable) officers when they do occasionally pull me over.
So the OP all sounds very dodgy to me - either they weren't real officers, or they were genuinely police officers but had been given some quite serious hard evidence of trafficking not mentioned in the original post.
Hadley xxx