I suspect, based on nothing more than a suspicion and some instructors anecdotes that it has declined
I think a problem faced is perception. I had my first lesson in 2010 and on turning up to a leaky portacabin, walking out to a faded, tatty 152 and hearing words like 'carburretor' made me wonder why I was risking my life on something so obviously dangerous and uncared for. A PPL friend explained a few things, recommended a tidier airfield with more cared for (albeit equally ancient) planes and I was soon hooked, and love my very tidy, well equipped almost new looking spamcan
We live in world of glitz and glamour, we all drive cars rarely older than 5-6 years, and expect instant gratification. Private flying doesn't compare favourably with these.
Also maybe society has moved in a bit from risk taking in hobbies. I mean, give massive amounts of time to get a licence, spend a fortune doing it and at the end of the day it can kill you ?
Sadly to an extent i worry this means the world has moved on (a little)from private flying.
I also wonder about the effect of austerity. I have mentioned to no-one other than my closest friends that I fly, and still fewer that I own an aircraft. Maybe a sad side effect of what the country has gone through is that we can no longer be proud of our achievements for fear of being seen as a bragger?