Hickox died Sunday of a heart attack in a hotel in Cardiff, Wales, said Stephen Lumsden, managing director of Intermusica Artists' Management Ltd.
Hickox had been due to conduct the new English National Opera production of Ralph Vaughan Williams' "Riders to the Sea," which opens Thursday.
He was musical director of Opera Australia, associate guest conductor of the London Symphony Orchestra, founder and music director of the City of London Sinfonia, co-director of the period instrument group Collegium Musicum 90, and conductor emeritus of the BBC National Orchestra of Wales.
"He was working with us yesterday on a CD recording in the Brangywn Hall Swansea, when he was suddenly taken ill," said David Murray, director of the BBC National Orchestra and Chorus of Wales. "As well as losing an inspiring conductor, we have lost a great friend and supporter."
Hickox was born into a musical family in Stokenchurch, England, on March 5, 1948.
After studying at the Royal Academy of Music and as an organ scholar at Queens' College Cambridge, Hickox in 1971 founded the City of London Sinfonia and the Richard Hickox Singers & Orchestra.
Hickox made more than 300 recordings for the Chandos classical record label.
He was music director at the Spoleto Festival in Italy for five years, where his productions included Richard Strauss' "Rosenkavalier," Leos Janacek's "Cunning Little Vixen," Sergei Prokofiev's "War And Peace" and Gian Carlo Menotti's "The Consul."
Hickox also conducted leading orchestras in Europe, Japan and the United States, including the Bavarian Radio Symphony, Leipzig Gewandhaus, Orchestre de Paris, the New York Philharmonic and the Philadelphia Orchestra.
He is survived by his wife, mezzo-soprano Pamela Helen Stephen, and three children.
Funeral arrangements were pending.