I work in a police control room and have done so for some 18 years now after a spell in airline ops.
Some of you would be surprised at how much we "non aviation" people know and we have a good set of operation orders to deal with aviation incidents.
I myself have been a radio controller for a number of them from simple force landings to fatal crashes.
I agree, call the police. We have the tel numbers for local airfields, D&D and other agencies as well as direct lines to coastguard, fire and ambulance. We will get the ball rolling, carry out searches and if the worst has happened protect and control the scene. Indeed only the other day I set the ball rolling when a member of public though he had seen an aircraft in difficulties perhaps making a forced landing. We later found out a similar aircraft had landed at Deanland not too far from the callers position so all ended well that day, as indeed most do.
In the case as quoted by Paul its likely we would have made a search in the area concerned although if near a coastal area we would have passed that to the coastguard for a sea search as well.
Cheers Ron