The eldest son of Robert Ellis Cunliffe [d. 1855] and his wife, Charlotte Howel [d. 1856], Sir Robert Alfred succeeded his grandfather as Baronet in 1859. He held many local official positions including Deputy Lieutenant, Justice of the Peace, and County Councillor for Denbighshire, and High Sheriff in 1868. He served as a Member of Parliament for Flintshire from 1872-74 and for Denbigh Boroughs from 1880-85. He was formerly a Captain in the Scots Guards and Hon. Colonel for the 3rd Battalion Royal Welsh Fusiliers. On 5 August 1869 he married Eleanor Sophia Egerton [d. 1898], daughter of Col. Egerton Leigh, Member of Parliament in Cheshire. They had two sons and three daughters. In 1901 he married secondly, to the Hon. Cecilie Victoria Sackville-West, Commander of the Order of the British Empire [d. 1955], daughter of Lt.-Col. Hon. William Edward Sackville-West and sister of the 3rd Baron Sackville. The two elder sons by his first wife, Foster Hugh Egerton and Robert Neville Henry, succeeded Cunliffe as 6th and 7th Baronets, respectively.