Morgan was born in Wimbledon, London. His mother, Inga (née Bojcek), was a Catholic Pole who fled the Soviets, and his father, Arthur Morgenthau, was a German Jew who fled the Nazis, arriving in London in 1933. His father died when Morgan was nine years old. Morgan attended boarding school at Downside School, Somerset, and gained a degree in Fine Art from the University of Leeds.