Pennine Boy, I share your concerns about the length of time it took for an ambulance to arrive on gate but this very probably had nothing to do with ATC, the airport authority or their procedures. Nor, necessarily, ambulance prioritisation. Do you know what other calls they were dealing with that day or what the traffic situation was like outside the airport?
Being an airport ATCO and having had to deal with such medical emergencies on several occasions I am sure the ATCO DID find the time to pick up the phone. As with other emergencies (including aircraft accidents) most airports have a clear procedure to follow.
At the airport I work at this involves using the direct "emergency line" to the Airport switchboard operator. They then, I hope, spring immediately into action and call the relevant services. One of the reasons it is carried out this way is our local switchboard understand what is going on when we have to keep saying standby because aircraft who are unaware of the fact I am on the phone keep calling - this might add confusion to a direct call to an outside agency. Once we have made this call we are confident an ambulance will be on its way! As to the use of AFS - we have been told this is not a legitimate use of AFS and as they are not under our control we have to respect that - although I'm sure many of us would call and suggest it.
I can assure you that if it took 50 mins plus for an ambulance to arrive at the gate the ATCO would have been just as frustrated - we are human beings too you know. Furthermore, I know of an ATCO who during one incident went beyond his remit and "demanded" attendance - he subsequently received a complaint from the Airport Authority and a one-sided interview from the boss!