Difficult to believe it had anything to do with ATC. I suspect that for a variety of reasons the airfield had to close at a particular time - safety services, aerodrome licence, etc. ATC is just one factor. I'm certain that if it had been possible to keep the airfield open the controller would have been only too happy to agree to a few minutes extension.
What worries me more is the fact that the ambulance had to drive to Bournemouth. Would it not have been possible to get a local ambulance from Bournemouth to take over?