ATC (in Scotland) will have a direct line to the local police control centre, who will in turn be in touch with the local hospitals/paramedical services.
In most cases, a request for the level of medical facility available at a given airport could be answered within a few minutes (provided everyone is on the ball - of course - but I can't see any reason why they shouldn't be!).
Do not hesitate to ask ATC for this type of information in an emergency; it's why we're here.