Robert Bankes was the son of Sir Robert Jenkinson, 2nd Bt., and his wife Sarah, daughter of Thomas Tomlins of Bromley. His brother who had succeeded as 3rd Bt. died without issue in 1717 and Robert succeeded as 4th Bt. On 12 June 1718 he married Catherine, third daughter of Sir Thomas Dashwood Bt; they had two sons, Robert and Bankes, who succeeded successively as 5th and 6th Bts. Sir Robert was Member of Parliament for Oxford between 1717 and 1727, following his father who had held the seat for many years. He died on 2 July 1738 and his wife died in March 1780.