Fancourt was born Darrell Louis Fancourt Leverson, the younger son of three children of a Jewish family in Kensington, London. His father, Louis George Leverson (1860–1909), was a diamond merchant who had made a fortune in South Africa. His mother, Amelia (Amy) de Symons, "née" Lewis-Barned (1865–1931), was "a clever vivacious young artist of the musical comedy type". Both were staunch friends of the arts. His father's sister married Brandon Thomas. Fancourt was baptised into the Church of England when he was fourteen years old.