I live in the Bath/Bristol area, and I've been on the lookout for a bass teacher. Everyone I've asked has recommended Bill Lynn, I've seen him play once and sat in at the end of that gig on trombone. He's a killer player, and reputedly a great teacher with a real passion for the instrument.
As for big name players in the area, as well as Keith Tippett and John Law, other prominent jazzers are Jason Rebello (currently on tour with Sting, but he is here usually) Mike Mower, ace saxophonist and flautist, Sax legend and former JB arranger/MD PeeWee Ellis, also Andy Sheppard tends to play in this area quite frequently. I think compared to most places theres quite a strong amateur scene as well, but I've never lived anywhere else so I don't know for sure

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Well worth checking out is the wiltshire music centre in Bradford-on-Avon, they quite often have good jazz gigs on, most recently the Out of the Darkness tour, featuring Law, Sheppard, Clarvis et al.
Jack Looman