Born in London in 1923, Parnell had showbusiness in his blood – his father Russ Carr was a music hall artist before becoming a theatrical agent, and his uncle ran a string of theatres. His grandfather Fred Russell was a ventriloquist.
Parnell showed promise for music at an early age. He started piano lessons as a four-year-old and after being sent away to boarding school began to take an interest in drums. He began drumming professionally as a teenager.
After a year with the Sammy Ash band at Cambridge's Rex Ballroom, Parnell volunteered for the RAF, hoping to become a military musician. There he became part of a band performing at the RAF Bomber Command HQ in High Wycombe. Their proximity to London also allowed Parnell and company ample opportunity to spend their nights in the capital to record and play for broadcasts.
When his time in the RAF came to end for medical reasons in 1944, Parnell joined the renowned Ted Heath jazz band before leading his own ensembles. His band Music Makers was full of great jazz players, including saxophonists Ronnie Scott and Pete King. Parnell's band toured Europe with Lena Horne to considerable acclaim in 1952, and backed Billie Holiday in a 1954 Royal Albert Hall concert.
Parnell came off the road in 1956 to take on the role of musical director for Associated Television (ATV). There he oversaw the music for the long-running variety show "Sunday Night at the London Palladium," produced specials featuring Tom Jones and Barbra Streisand, composed theme tunes for programmes such as Family Fortunes and served as musical director of "The Benny Hill Show."
In 1976, ATV began producing "The Muppet Show". Parnell conducted the orchestra – the "real" band for The Muppet Show – for the whole of the series' five-year run.
Parnell retired from ATV in 1982 when it became Central Television, but continued to perform with bands near his home in Southwold, Suffolk until three years ago.
Parnell died just two days after his 87th birthday. He is survived by his wife Veronica, two daughters and three sons — two of them drummers.