The Liverpool native was unable to go to university for financial reasons so ended up working in an insurance office for six years before joining Preston Rep as an assistant stage manager. Rossiter made his acting debut on the London stage in 1958 and quickly moved into British films, appearing in secondary roles in some of the classics of the 1960s. More remembered for his comedic work, Rossiter turned in consistently standout performances. He played the title character's insufferable, unctuous boss in "Billy Liar", was an English Major dealing with the tensions of his fellow prisoners in a Japanese POW camp in "King Rat", offered a luscious turn as Mr. Sowerberry in "Oliver!" (1968), and was a rich British officer who thwarts the boyhood love interest of the title character in Stanley Kubrick's lavish "Barry Lyndon" (1975).
Blake Edwards tapped him twice to play Superintendent Quinlan in "The Pink Panther Strikes Again" (1976) and "Trial of the Pink Panther" (1982) but it was probably Lindsay Anderson's satire of England "Britannia Hospital" (1982) in which Rossiter, starring as the put upon hospital administrator, was at his loony best. He was also a standout in his final film, the uneven comedy "Water" (1984) where he played a stuffy, mindless British bureaucrat sent to straighten out the chaotic situation on a Caribbean island colony.
Rossiter also made appearances on British television and it was the 1976 series "The Fall and Rise of Reginald Perrin" that made him a household name in Britain. He played an executive who tried to alter his dreary day-to-day life by launching his own company which sold "gifts for people you hate". Frequently returning to the stage through out his career, he was playing the role of the detective in a 1984 London production of Joe Orton's "Loot" when he failed to make an entrance and was discovered dead in his dressing room, an apparent heart attack.