Quite a few AMEs around the south of London have recently retired, including my AME, I hear that there are a couple of practices that are still currently running that are also considering closing within the next few years.
Are they diminishing, in my eyes yes, but perhaps all the AMEs just work part time out of the big centre at Gatwick!
I keep telling my other half (who is a doctor), to consider becoming an AME, but although she loves flying with me, she has no real interest in the aviation industry which is a barrier to become an AME (not really sure why - although an interest is definitely a good thing, they don't do much more than a set of required tests which surely could be done by any competent doctor with the mandatory training that the CAA provides). It looks as though you either need to have a Pilot's Licence (£10,000 +), or do a 1 year full time course at KCL (which costs £27,750).
Perhaps these barriers are somewhat too strenuous to attract new, younger doctors to the AME field.
(or perhaps they all buggered off to Australia to get a fair wage & fair timetable!)