The son of Sir Foster Cunliffe, 3rd Bt., and his wife, Harriet Kinloch, Sir Robert succeeded hsi father as Baronet in 1834. He was a Companion of the Order of the Bath and served as a General in the Bengal Army. In 1829, he was knighted for his services. On 15 December 1805, he had married Louisa [d. 1822], widow of Major Arthur Forest, and had (with other issue) three sons. Cunliffe married secondly in 1825 to Susan Emily [d. 1856], daughter of Col. John Paton, Commissary General of the Bengal Army, and by her had (with seven other daughters), four more sons. His grandson, Sir Robert Alfred Cunliffe, succeeded him as 5th Bt.