Hard data is hard to come by, but some is available.
As a starter: some statistics from the UK CAA
with respect to registered aircraft and
with respect to issued licenses (includes renewals).
W.r.t. aircraft registered, it shows a healthy growth in microlights and a recent decline in typical spamcan-type aircraft, albeit after a better growth up to 2008, so still an increase compared to 1985.
W.r.t. licenses, the format reported has changed, as have the license categories, so it's not obvious to get a like-for-like comparison. But there is a decline.
Neither of these seem to be the 'off the cliff' and 'death of GA' which seems to be often referred to, but a clear decline nevertheless.
And, of course, they do not tell how many hours are flown.
Mayday/PAN events may serve as an indicator either of fewer emergencies or of reducing activity - but then again,
this would show an increase.
Individual airfields (and LARS units, I assume) track their movements and would be a better measure of 'busy-ness' , but I don't know whether such data are ever made public or where to look for them. Ditto for the hours flown which are part of the info provided for the medicals.
I'd love to hear if there are other public sources of data out there ...
(Other countries probably publish similar information as the UK CAA, I'd think)
B.