Cotton married Frances Stapleton, daughter and co-heiress of James Russel-Stapleton Esq in 1767. In 1774 they were visited at Llewenli Hall by Sir Robert's cousin, Hester Thrale, who was accompanied by the noted writer, Samuel Johnson; Frances "found Johnson, despite his rudeness, at times delightful, having a manner peculiar to himself in relating anecdotes that could not fail to attract old and young. Her impression was that Mrs. Thrale was very vexatious in wishing to engross all his attention, which annoyed him much". The Cottons later broke off relations with Hester following her 1784 marriage to an Italian music teacher. In 1774 he was elected a Fellow of the Royal Society. On the death of his father on 14 August 1775 he succeeded to the baronetcy and inherited the old Salusbury family seat at Lleweni Hall. Soon after the birth of his second son he moved from Lleweni Hall to Combermere Abbey, the traditional seat of the heir apparent to the Baronetcy. He had to lease the family's former estate to the Hon Thomas FitzMaurice, a brother of Lord Shelburne's, because of the profligacy of his uncle, Sir Thomas. Nevertheless, Sir Robert kept a large hunting establishment and was known as a generous host.
Parliamentary career
Cotton was returned unopposed as Member of Parliament for Cheshire at a by election on 1 March 1780 and at the succeeding 1780 general election. In 1784 he was a member of the St. Alban's Tavern group who tried to bring Fox and Pitt together. He was returned again unopposed in 1784 and 1790. Towards the end of that parliament he applied three times to Pitt for the position of collectorship of salt duties at Nantwich and was ignored. It was unexpected when he decided not to stand at the 1796. His brother writing later said it was through ill-health and that he had declined a peerage, but contemporary accounts claimed it was in annoyance at not being given the post.
Later life and legacy
Cotton was a major in the Nantwich volunteers in 1797 and 1803. He had to sell his Welsh estates for about £390,000 as he was in debt through extravagance and bad management. He died aged 70 on 24 August 1809. Cotton and his wife Frances had the following children:
Robert-Salusbury, died without issue
Stapleton, 6th baronet, elevated to the peerage as a Viscount and Baron Combermere