His brother Bernard Babington Smith OBE (1905–1993) was an academic, wartime intelligence officer and amateur athlete.

[1][4] Babington Smith was part of the Officer Training Corps at Cambridge and was commissioned into the Territorial Army as a 2nd Lieutenant in the Leicestershire Yeomanry, in 1925.

In 1943, he was recalled to England to serve as an assistant to US Army General Dwight D. Eisenhower at Supreme Headquarters Allied Expeditionary Force (SHAEF).

Promoted to Brigadier, Babington Smith was Director of Finance at SHAEF until 1945, tasked with planning the financial aspects of the Allied invasion and subsequent administration of Western Europe.

[1][4] In April 1945, Babington Smith was named a Commander of the Order of the British Empire, military division, for his service during the Second World War.

[1] In 1990, his widow was raised to the rank of an earl's daughter by royal warrant, entitled to be styled as Lady Jean Babington Smith.