During my time at Heathrow I must have dealt with many hundreds of ambulance, organ-carrying or sick-passenger flights. All I can recall is simply being told by a supervisor that XXX was a medical flight or being advised by the pilot. I don't recall any flight having Cat A status except the HEMS helicopter when involved in serious accidents (see Talkdownman's post). Sick passengers on commercial aircraft are a way of life but I never knew one to be afforded Cat A status. Nevertheless, when we were notified of a medevac of any sort we would bend over backwards to give it priority.
My advice would be to phone the ATC unit at your destination and advise them.