Hickox was born on the 5th
of March, 1948 in Stokenchurch in Buckinghamshire into a musical family. After attending the Royal Grammar School in High Wycombe from 1959 to 1966, he studied at the Royal Academy of Music in London from 1966 to 1967, before becoming an organ scholar at Queens' College, Cambridge from 1967 to 1970.
In 1967, while his father was Vicar of Wooburn, Buckinghamshire, Richard founded the Wooburn Festival and eventually became its President. The Festival is ongoing and features music, drama and the visual arts. Richard also founded the Wooburn Singers and continued as conductor until succeeded by Stephen Jackson. Hickox 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 feature in Kate Bush's album Hounds of Love, released in 1985. He was the director of music at the St. Endellion Music Festival from 1972 to 2008. In 1972 at the age of only 24 he was appointed Martin Neary's successor as organist and master of music at St. Margaret's, Westminster (the church of the Houses of Parliament), subsequently adding the directorships of the London Symphony Chorus (1976) and Bradford Festival Choral Society (1978). From 1982 to 1990, he served as Artistic Director of the Northern Sinfonia. He was Associate Guest Conductor of the London Symphony Orchestra from 1985 until his death in 2008. He was also Chorus Director of the London Symphony Chorus from 1976 to 1991, with whom he premiered The Three Kings by Peter Maxwell Davies in 1995. He also premiered A Dance on the Hill in 2005, by the same composer. His repertoire included over 100 first performances.
In 1990, he co-founded the baroque orchestra Collegium Musicum 90 with Simon Standage. For five years, Hickox was Music Director of the Spoleto Festival, Italy. From 2000 to 2006, he was Principal Conductor of the BBC National Orchestra of Wales, thereafter becoming its Conductor Emeritus. He became the Music Director of Opera Australia in 2005, and in this role he conducted the Australian premieres of The Love for Three Oranges, Rusalka, and Arabella (which won 2008's prestigious Helpmann Award for Best Opera). He also collaborated on new productions of The Tales of Hoffmann and Alcina. Hickox also led major revivals, including Tannhäuser, Death in Venice, Giulio Cesare, Billy Budd, and Janácek's The Makropulos Affair. Hickox was contracted as Opera Australia's music director through 2012 at the time of his death in November 2008.
Hickox was appointed a Commander of the Order of the British Empire (CBE) in the 2002 Queen's Birthday Honours. In 1997 he won the Grammy Award for Best Opera Recording for his recording of Britten's Peter Grimes. He won five Gramophone Awards: for recordings of Benjamin Britten's War Requiem (1992); Frederick Delius's Sea Drift (1994); William Walton's Troilus and Cressida (1995); Ralph Vaughan Williams' A London Symphony (2001 Record of the Year and Best Orchestral Disc); and Charles Villiers Stanford's Songs of the Sea (2006 Editor's Choice). He made only the second recording of Delius's Requiem (1996).
He was awarded a Doctorate of Music at Durham University in 2003; and was an Honorary Fellow of Queens' College, Cambridge. He received two Royal Philharmonic Society Music Awards, the first Sir Charles Groves Award, the Evening Standard Opera Award, and the Association of British Orchestras Award. He was also President of the Elgar Society.