After Hot Ptah recognized Tubby Hayes and suggested it was from the late 60s, it wasn't too hard for someone with a copy of Simon Spillett's biography of Hayes (which includes a discography) and Spotify at their disposal to put two and two together.
I think it's "Greenwell's Glory" by the Ian Hamer Sextet featuring Hamer (tpt), Keith Christie (tbn), Hayes (tnr), Alan Branscombe (elp), Daryl Runswick (bg) and Spike Wells (dms), recorded at BBC Studios, London on 2nd July 1972.