Educated at Dulwich College, southeast London, Rich became involved in acting from an early age, making his theatrical debut in 1923. He was subsequently involved in theatre for several years. During the Second World War, he was standing in as a news announcer when Broadcasting House was hit by a bomb during the 9pm news broadcast.
In 1964, he became head of British Broadcasting Corporation Light Entertainments (Sound), a post which he held until his retirement in 1967.
Rich died from cancer in hospital in Stratford-upon-Avon in 1970, aged 57.
He was a pioneering broadcaster for the British Broadcasting Corporation, as one of the first radio DJs.