Dunbar was born in Mexico City in 1943, the son of the British filmmaker Robert Dunbar. He has three sisters, Marina Adams, an architect, and twins Margaret and Jennifer Dunbar. He spent his first four years in Moscow, where his father was a cultural attache, before the family returned to England. Dunbar attended the University of Cambridge, where he met the singer Marianne Faithfull. They were married on 6 May 1965, with Peter Asher as the best man, and spent their honeymoon in Paris, with the Beat poets Allen Ginsberg and Gregory Corso. The couple lived in a flat at 29 Lennox Gardens, Knightsbridge, London. On 10 November 1965, she gave birth to their son, Nicholas. Dunbar and Faithfull divorced in 1970, with John winning custody of his son.
