Well firstly I would separate the US West Coast Acid Rock and Psychedelic Punk from the true British Psychedelic Bands.
In the late sixties the use of LSD sparked a huge change in music in Britain. Lots of groups started experimenting with sound and going psychedelic.
It is consequently very difficult to separate out what is a psychedelic band from that of a Progressive Rock band. A lot of the established bands (Beatles, Stones, Yardbirds, Animals, Pretty Things, and even the Hollies and Status Quo) took on a psychedelic period. Some other of the newer bands mixed psychedelia with other styles. So Soft Machine, a Jazz fusion band had psychedelic elements. Not to worry. I’ll include them all.
During that period in 1967-70 I managed to see all of these bands like at places such as Middle Earth, UFO and the Marquee, as well as at all-nighters and festivals. Some great light shows (Tomorrow were particularly good with the first use of strobe that I’d seen) and stage antics.
Psychedelia was great.
So my favourites were:
Jimi Hendrix Experience
Incredible String Band
Edgar Broughton Band