Born in London in 1909, Peter Graham read History and English at Magdalen College, Oxford, graduating in 1931. He became a schoolmaster following his degree and it wasn’t until he was twenty-six that he started attending art classes at Byam Shaw School of Drawing and Painting. Studying under F.E. Jackson, he became an excellent draughtsman. Byam Shaw closed during the Second World War and he returned to teaching, this time at Magdalen College School in Oxford. At this point, he was exhibiting at the Royal Academy, becoming an associate in 1951 and a Royal Academician in 1960. He was made Keeper of the Academy in 1964, the same year he married fellow painter, Irene Mary Dowling, and he served in this position until his retirement in 1985. He was appointed CBE in 1978.

Greenham was a painter of both portraits and landscapes. As Keeper of the Royal Academy for twenty-one years, he ran the school in a relaxed manner but one which was based on deeply-held convictions such as always stressing the importance of life drawing when other art schools were abandoning traditional methods.