Born in London, England in 1921, Farrar was the elder son of Donald Frederic Farrar (1897-1982), a former Royal Flying Corps supply pilot, and Mabel Margaret Farrar, née Hadgraft (1896-1985), and brother of RAF airman and poet James Farrar.
He was educated at Sutton Grammar School for Boys, Surrey, and won three scholarships to Cambridge University, going up in 1939 to Gonville and Caius College.