An old friend of mine used to work for a People Tracing company. One of his "Tricks" was something along these lines -
He would ring around local doctor's surgery asking if they had a patient named whoever. He, the caller was Dr. Smith who needed to pass on important medical information to John Doe's new doctor but he had lost the contact details. To sound authentic, the caller would ask to be called back at "His Surgery" and give the number of a surgery he had looked up.
He would then contact this second surgery, say he was Dr Smith with an appointment later that day but might be delayed. He was expecting an urgent call and had given their number. If he was late, would they mind taking the message and call him on his mobile.
He used a variation on a theme with job centres, N.I. records etc. A bit convoluted but they were serious people tracers.