Heckstall-Smith was an active member of the London jazz scene from the late 1950s. He joined Blues Incorporated, Alexis Korner's groundbreaking blues group, in 1962, recording the album R&B from the Marquee. The following year, he was a founding member of that band's breakaway unit, The Graham Bond Organization. (The lineup also included two future members of the blues-rock supergroup Cream: bassist Jack Bruce and drummer Ginger Baker.)