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During the 1940s and 1950s, he was voted best drummer in the Melody Maker poll for seven years in succession. He composed many television themes, including Love Story (for which he won the Harriet Cohen Award), Father Brown, The Golden Shot and Family Fortunes. He was a regular judge on the ATV talent show New Faces. He was also the musical director for The Benny Hill Show.
He was appointed musical director for ATV in 1956, a post he held until 1981, and served as the 'real' conductor for The Muppet Show orchestra for the entire series and even composed the bombastic brass score theme to ITC Entertainment.
He was jailed for three months for a drink-driving accident in 1979, hitting a motorcyclist who lost a leg. After this he moved from Surrey in disgrace and shortly after his wife divorced him.
From 1991 until he died, Parnell was part of the Norfolk-based Mike Capocci trio, with Mike on piano and Mike Harris on the double bass. They backed the likes of Tubby Hayes, Ronnie Ross, Kathy Stobart and Johnny Griffin.