Francis Annesley (2 May 1734 – 17 April 1812) was an English politician who sat in the House of Commons for 32 years from 1774 to 1806, and was the first Master of Downing College, Cambridge.He was educated at Reading School and was admitted at Gray's Inn in 1753 to study law.[2] In 1800 he was elected the first Master of Downing College, and awarded an LL.D.Their daughter, Frances Cotton, married John Hanbury, and was mother to Mary Hanbury, who was Annesley's mother.[3] He was heir to Sir George Downing, 3rd Baronet, but the effective founding of Downing College was long delayed by litigation with other parties, in which he was heavily involved.