Heckstall-Smith was born Richard Malden Heckstall-Smith in Ludlow, England (his father then being headmaster of the local Grammar School), and brought up in Knighton, Powys. He learned to play piano, clarinet and alto saxophone in childhood.
After refusing a second term at a York boarding school, he went to Gordonstoun Scotland, where his schoolmaster father, Hugh, had taken a job. Hugh soon fell out with the autocratic Kurt Hahn and the family retreated to Dartington.
Heckstall-Smith completed his education at the Foxhole school before reading agriculture – and co-leading the university jazz band – at Sidney Sussex College, Cambridge, from 1953. Aged 15, he had taken up the soprano sax while at Foxhole, captivated by the sound of Sidney Bechet. Then the smokiness of Lester Young's sound caught him, and the music of tenor saxist Wardell Gray, a major early bebop musician.
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 Organisation; the lineup also included two future members of the blues-rock supergroup Cream: bassist Jack Bruce and drummer Ginger Baker.
In 1967, Heckstall-Smith became a member of keyboardist-vocalist John Mayall's prominent group the Bluesbreakers. That jazz-skewed edition of the band, which also included drummer Jon Hiseman and future Rolling Stones guitarist Mick Taylor, released the album Bare Wires in 1968.
From 1968 to 1970, Heckstall-Smith and Hiseman were the key creative members of the pioneering UK jazz-rock band Colosseum. The act was a showcase for the saxophonist's writing and his instrumental virtuosity; like American saxophonist Rahsaan Roland Kirk, he could blow two saxophones simultaneously.
After exiting Colosseum, Heckstall-Smith fronted several other fusion units, including Manchild, Sweet Pain, Big Chief, Tough Tenors, The Famous Bluesblasters, Mainsqueeze and DHSS. Collaborating musicians common to many of these outfits included Victor Brox, Keith Tillman and particularly harp player John O'Leary, a founder member of Savoy Brown. He participated in a 1990s reunion of the original Colosseum lineup and played the hard-working Hamburg Blues Band. In 2001 he cut the all-star project "Blues and Beyond", which reunited him with Mayall, Bruce, Taylor, ex-Mayall and Fleetwood Mac guitarist Peter Green.
Recorded in April 1972, "A Story Ended" was the debut solo album by Colosseum saxophonist Dick Heckstall-Smith. Recorded upon the demise of Colosseum, the sessions featured contributions by Jon Hiseman, Mark Clarke, Chris Farlowe & Dave Greenslade of the band, along with Graham Bond (of whose Organization Dick was a member alongside Jack Bruce & Ginger Baker), Chris Spedding and lyrical offerings from Pete Brown. A superb example of Jazz influenced Progressive rock, the album appeared on Bronze Records in 1972 and is now hailed as a classic of the genre.