The fascinating story is covered in a new video DVD Going Underground: Paul McCartney, the Beatles and the UK Counter-Culture (Pride DVD161). It follows both the development of the alternative culture and Paul's involvement chronologically with a narrative that incorporates archival footage and personal interviews with some of the figures that were a part of the scene, for an in-depth 153 minutes.
There's so much covered here that I can't begin to inventory it all, but it tracks the underground press and its sponsoring of/involvement with an extension of beat culture, identity politics and the avant and psychedelic music scenes. In essence Paul got turned on to the avant improv band AMM and various new sounds as he absorbed some of the underground ethos. He also attended and helped support the opening of the first of the psychedelic clubs, where Pink Floyd and Soft Machine got their starts.
There are sections of the DVD that talk about how all this influenced some of the pioneering Beatles cuts such as "Tomorrow Never Knows," "A Day in the Life" and "Strawberry Fields."
It's something anyone interested in the psychedelic musical movement, the classic Beatles art-music period, and the counter-culture in general will profit by seeing. I found it pretty riveting. Worth it alone just for the interview with Robert Wyatt, the Soft Machine's seminal first drummer!