Goddard was born in Bicester, Oxfordshire. He played Mr. Bumble in two versions of Charles Dickens's Oliver Twist – a 1962 television adaptation, and the original Broadway production of the musical Oliver!. He originated the role of Cardinal Wolsey in the West End production of Robert Bolt's A Man for All Seasons. He appeared in the television series The Adventures of william Tell (which lasted 39 episodes) in 1958 and 1959 as the villain Landburgher Gessler; and as Reeder's boss, Sir Jason Toovey (who was head of the Department of Public Prosecutions) in The Mind of Mr. J. G. Reeder, a TV series of 16 hour-long episodes with first season 1969 and second season 1971; also as Sir Geoffrey in The Man in Room 17, which ran two series of 13 hour-long black-and-white episodes in 1965 and 1966.