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Moving to London after the Second World War, Sykes began his entertainment career writing for radio, including the classic BBC comedy series The Goon Show, before successfully transitioning to film and television in the 1950s. Between 1960 and 1965, he appeared alongside Hattie Jacques in the sitcom Sykes and A..., which he co-created with Johnny Speight, with Sykes and Jacques subsequently appearing in the follow-up series Sykes (1972-1979). Sykes would also collaborate with Speight on the short-lived sitcoms Curry & Chips (1969) and The Nineteenth Hole (1989), as well as making a guest appearance in Speight's best-know series Till Death Us Do Part in 1970.
Having suffered hearing problems for most of his adult life, Sykes' eyesight began to fail him in the 1990s, although he continued to remain active, with later credits including film roles in The Others (2001), Harry Potter and the Goblet of Fire (2005) and Son of Rambow (2007), as well as guest appearances in TV shows such as dinnerladies, My Family, Heartbeat and Agatha Christie's Poirot.