Richard Fletcher was the eldest child and only son of Alexander Kendal Humphrey Fletcher, a banker from Leeds, by his marriage to Monica Elizabeth Hastings Medhurst/Fletcher. His childhood home was at Wighill, near Tadcaster. He attended, as a scholar, Harrow School and Worcester College, Oxford where he was taught by James Campbell and achieved a First Class Honours degree.
In 1969 he was appointed as a lecturer at the University of York where he remained for the rest of his career, becoming professor of history in 1998. His first book, published in 1978 and based on his doctoral thesis, was entitled "The Episcopate in the Kingdom of León in the Twelfth Century", which pointed the way for an academic career much of which would focus on medieval Spain. Fletcher was one of the outstanding talents in English and Spanish medieval scholarship.
Richard Fletcher married Rachel Mary Agnes Toynbee, herself a grand daughter both of another notable historian and of a British Liberal prime minister, in 1976. The marriage produced three children.