Francis Murphy studied at Camberwell School of Arts and Crafts and the Royal Academy.
He has been awarded many prizes including the David Murray Prize 1976 and 1978, the Royal Overseas League Prize 1978, the British Institution Prize 1978, the Imperial Tobacco Award at the National Portrait Gallery 1983, the Spirit of London Competition 1985 and 1986 (a prize winner both years). He won several prizes while a student at the Royal Academy.
He has exhibited at numerous galleries. He was included in the Royal Academy of Arts Summer Exhibition on ten occasions. Collectors of his work include Michael Gambon, the actor, who commissioned a portrait and bought other works, Lord Gowrie, former Arts Minister and Chairman of Sotheby's, and the former British Ambassador to Columbia.