Brother of the artist Robert Duckworth Greenham. Educated at Dulwich College and won a scholarship to Oxford to read history, even though in the end read English. Studied at Byam Shaw School of Drawing and Painting under Ernest Jackson in 1935-39. Elected RA in 1960. Greenham succeeded Sir Herbert Rushbury as the keeper of the Royal Academy Schools in 1964 until his retirement in 1985.Showed widely in mixed exhibitions and from 1972 had many solo shows at New Grafton Gallery. Tate Gallery holds his work. In 1984/85 Arts Council and Norwich School of Art put on a touring show of his work.