The son of Sir Robert Alfred Cunliffe, 5th Bt., and his first wife, Eleanor Sophia Egerton (daughter of Col. Egerton Leigh, Member of Parliament), Sir Foster succeeded his father as 6th Baronet in 1905. He earned a Master of Arts at New College, Oxford, where he was a Fellow of All Souls and sometime Lecturer in military history. He served as a Temporary Major of the 12th Battalion Rifle Brigade, and was killed in action in 1916, whereupon his brother, (Sir) Robert Neville Henry Cunliffe, succeeded him as 7th Bt.