Don’t sweat over it, there’ll not be any black mark against your name or anything like that, and unless there’s any strong evidence there’ll be nothing to defend yourself against (and I’m sure this would have been mentioned when you were stopped if there was).
Where I work we probably get half a dozen complaints a day at this time of year about erratic or dangerous driving. If we can trace the car then we’ll stop it, say hello to the driver, make sure they don’t stink of booze, check insurance if it’s not a hire car (90% are for these complaints), and off they go after a couple of minutes.
the police don’t have the authority to stop and check your documents unless you do something
Aye they do, they can stop any vehicle to check your driving licence, insurance and MOT. You don’t have to have done anything wrong, and they don’t have to give a reason for stopping you.
Stop and search requires grounds for the search of course, they shouldn’t be random, but not a straightforward vehicle check.