Heckstall-Smith was born in the Royal Free Hospital, in Ludlow, Shropshire, England,[2] and was raised in Knighton, Radnorshire, learning to play piano, clarinet and alto saxophone in childhood.

[1] Heckstall-Smith completed his education at Dartington Hall School, before reading agriculture – and co-leading the university jazz band – at Sidney Sussex College, Cambridge (1953–1956).

[4][5] Heckstall-Smith was an active member of the London jazz scene from the late 1950s (including a six-month stint from December 1957 with the band led by clarinettist Sandy Brown).

[7] When Colosseum broke up in October 1971, Heckstall-Smith recorded solo albums (1972's A Story Ended featuring lyrics by Pete Brown)[7] and fronted and played in 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 harp player John O'Leary, a founder member of Savoy Brown.