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Suffield was the eldest son of Charles Harbord, 5th Baron Suffield, and his first wife Cecilia Annetta, daughter of Henry Baring, third son of Sir Francis Baring, 1st Baronet.
A member of the influential Baring family, he was the son of Lieutenant-General Charles Baring, son of Henry Bingham Baring, son of Henry Baring, third son of Sir Francis Baring, 1st Baronet.