Greenslade was born at Formby in Lancashire. During the Second World War, he served as a Lieutenant commander in the Royal Naval Reserve for two and a half years, and was then a purser with the P&O Line before joining the BBC in 1945.

His BBC career began in the European Service, where he was a presentation assistant and news reader. In 1949 he was appointed announcer, Home Service and since November 1955 he had been a news reader in both radio and television.

He worked in a variety of shows during and after his time on the Goon Show (1953 - 1960).

Wallace died in 1961, just over a year after the final series of The Goon Show had ended.