Coke (pronounced Cook) was the son of the Honorary Arthur George Coke, who was killed in action in 1915 during World War I. He was the second son of Thomas Coke, 3rd Earl of Leicester and of Phyllis Hermione, daughter of Francis Saxham Elwes Drury.
He was educated at Gresham"s School in Holt, Norfolk.
During World World War II, Leicester served in the Royal Air Force. After the war,in the late 1950s, he became a Land Development Officer (LDO) in Rhodesia, attached to what was then known as the Native Affairs Department (later known as the Internal Affairs Department).
