Remfry moved to Hull aged five and attended Hull College of Art from 1959 to 1964 before moving to London. His first solo show was in London at the Grafton Gallery in 1973 and in the United States at the Ankrum Gallery, Los Angeles in 1980. He has exhibited since then at galleries in London, Holland, New York, Los Angeles and Florida. In 2002 Alanna Heiss curated a show of his work at MOMA, New York. Other exhibitions include the Boca Ratan Museum of Art, 1999 and 2002 Butler Institute if American Art 2003, Ohio, and the Museum of Art Deland, 2017 Orlando.
Solo museum shows in the UK include the Fitzwilliam Museum, Cambridge Ferens Art Gallery Hull, (1975 and 2005), Middlesbrough Art Gallery, the National Portrait Gallery and the Victoria and Albert Museum, London. The National Portrait Gallery commissioned Remfry to paint Sir John Gielgud in 1981 and also acquired his watercolor of Jean Muir.