Francis Wyndham was born in London in 1924 to Violet Lutetia Leverson and Guy Percy Wyndham. His mother was the daughter and biographer of the writer Ada Leverson (a friend of Oscar Wilde, whom Wilde called "Sphynx"). His father was a retired soldier and diplomat, had been a member of "The Souls", and was significantly older than his mother ("more like a grandfather really"). Francis also has a brother and, from his father's earlier marriage, a half-brother and half-sister, the photographer Olivia Wyndham (another son from this earlier marriage had died in the First World War).
He graduated from Eton in 1940, spent a year at Oxford University and then was drafted into the army in 1942 until it was discovered he was suffering from TB. He was discharged and returned to London, where he began writing reviews for The Times Literary Supplement and short stories (collected in Out of the War). From 1953 he worked in publishing, first for Derek Verschoyle and then for André Deutsch as a reader (where he became involved with the writing careers of, and friends with, Bruce Chatwin, V. S. Naipaul, Jean Rhys and Edward St Aubyn). He left to become an editor at Queen magazine and in 1964 was hired by The Sunday Times (moving with his friend Mark Boxer), where he stayed until 1980. He became Jean Rhys' literary executor after her death in 1979.