Educated at Sherborne School, Percival first became well known for performing topical calypsos on television satire shows such as That Was The Week That Was. He appeared in the Carry On film, Carry On Cruising (1962). He also provided the voice of central character "Old Fred" in The Beatles' animated film Yellow Submarine, and the 'voice' of both Paul McCartney and Ringo Starr in the 1965 cartoon series based on The Beatles, simply entitled The Beatles. In 1963 Percival had a cameo role in the film, The V.I.P.s. 1964 saw Peter Tinniswood collaborate with long-term writing partner David Nobbs on the BBC TV comedy Lance At Large, starring Percival.
He is also the author of books of verse, Well-Versed Cats and Well-Versed Dogs which are both illustrated by Lalla Ward. In 1970 he starred alongside Julie Andrews, Rock Hudson and Jeremy Kemp in the musical film, Darling Lili,
He also has one UK Singles Chart hit, reaching #37 in October 1965 with his cover version of a calypso-style song entitled, "Shame and Scandal in the Family".
Between 1972 and 1978 the Thames Television game show, Whodunnit! was written by Percival and Jeremy Lloyd.