Hickox was born in Stokenchurch in Buckinghamshire into a musical family. After attending the Royal Grammar School, High Wycombe from 1959 to 1966, he studied at the Royal Academy of Music in London from 1966 to 1967, then was an organ scholar at Queens' College, Cambridge from 1967 to 1970. In 1967, while his father was Vicar of Wooburn, Buckinghamshire, Hickox founded the Wooburn Festival and eventually became its President. The Festival still takes place and features music, drama and the visual arts. Hickox also founded the Wooburn Singers and continued as conductor until succeeded by Stephen Jackson. From 1970 to 1971 Hickox was Director of Music at Maidenhead Grammar School (later Desborough School). He founded the City of London Sinfonia in 1971, remaining music director until his death, and also founded the Richard Hickox Singers and Orchestra in the same year. The Richard Hickox Singers are featured on Kate Bush's album Hounds of Love...