Francis Cockayne Cust (1722 – 30 November 1791) was a British lawyer and politician who sat in the House of Commons between 1770 and 1791.
He suffered from deafness which interfered with his professional career but obtained good practice as a Chancery lawyer.
He was invited to stand at Helston by the party opposed to the Godolphin interest, on condition that if defeated he would petition.
He and Philip Yorke of Erthig, a son-in-law of John Cust, were seated for Helston in March 1775 on a petition which impugned the working of the new charter given to the borough by the Government on 3 September 1774.
He mistakenly believed that Lord Auckland intended to resign the auditorship of Greenwich Hospital, a place worth £100 p.a.