I would suggest that the 'oxbridge' of the flight training world would be the RAF's central flying school at cranwell.
Looking at the RAF's central flying school website they say
"To train flying instructors, test individual aircrew, audit the Flying Training System, give advice on flying training, and provide the RAF Aerobatic Team."
Not sure 'oxbridge' really do this kind of thing, well maybe the instructor training but this would be way off someone looking to start out!
