This isn't really going to work or be a major issue for Drone pilots until November when all drone users (over the weight limit) are going to need to carry and show registration on their drones ... Otherwise, what are they searching for? It's not like you are flying your drone with it concealed in your Jumper!
I don't think this is going to be based on 'complaints' - unless the complaint accuses the Drone Pilot of violating CAA reg's, and the Officer attending doesn't get to see registration paperwork (post November).
That said ... I think this is mainly to combat the misuse of Drones near an Airport ... The Police need something that gives them the rights to search for a drone in a back-pack, if they are trying to chase perpetrators when there has been an incident like at Gatwick. The ability to put a Mavic in a lunch-box means that it's pretty easy to conceal and there has to be some legislation that allows the Police to stop and search if they have suspicions. If you are unlucky enough to be in the vicinity of a 'Gatwick-like' incident, and you have your 'innocent' drone in the back of the car - then that is going to be a tough one ... The question is going to be "Do they take your word for it when you show the flight logs?"