the primary purpose for gatherings relating to music is the perpetuation of the music

Well, I would say that the primary purpose for gatherings relating to music is to have fun, not to bolster a sociological principle. And to say that sessions in pubs don't count is sheer nonsense.

I was also a musician in London in the 1960s and, as with Don Firth above, we musicians gravitated to places where good music was to be heard - and it was rarely in the spontaneous, sitting-around-in-open-spaces setting you describe (and I lived in Bayswater, very close to Kensington Gardens and Hyde Park). It was in clubs like the Cousins, the Troubadour, Bunjies, the Marquee, Klooks Kleek, and in pubs like the Scots Hoose, the Half Moon and so on.

There were, of course, hugely popular free concerts in Hyde Park - concerts which cost absolutely nothing for the listeners - and I went to the first 2 or 3 of those. The first one (1969 I think) featured Fairport Convention, Peter Green's Fleetwood Mac, The Family, Ten Years After, Roy Harper, etc., and was an amazing experience. But it wasn't spontaneous - it was very carefully organised, with superb musicians playing for nothing. And it wasn't to "perpetuate the music" - it was sheer, unalloyed fun.