Parnell was born into a theatrical family in London, England. His uncle was the theatrical impresario
Val Parnell. During his military service in the 1940s he became a member of
Buddy Featherstonhaugh’s Radio Rhythm Club Sextet and played drums with
Vic Lewis and other servicemen who were keen on jazz. From 1944 to 1946 Parnell recorded with Lewis, and the Lewis-Parnell Jazzmen’s version of "Ugly Child". During the 1940s and 1950s, he was voted best drummer in the
Melody Maker poll for seven years in succession. He was appointed as the
musical director for
ATV in 1956, From 1991 until he died, Parnell was part of the Norfolk-based Mike Capocci Trio, with Capocci on piano and Mike Harris on the double bass. They backed saxophonists
Johnny Griffin,
Ronnie Ross, and
Kathy Stobart. In 1994, he took over as the leader of the London Big Band, which comprised some of Britain's leading jazz musicians. ==Personal life and death==