I can't believe that any UK ATCO would do this ifindeed was a properly filed medivac flight.
I think that all of us would have stayed on for as long as needed then filed a STRACOH report, equally, the same applies to all the AFS staff at all the airports I've previously worked at.
If, however, Auriegny had failed to make the Duty Manager at Southampton aware that it was indeed such a flight and the pilot failed to declare it as such, then there's only so long I would expect the Fire Service, or anyone else, to wait.