Delmé was from a wealthy Huguenot family, and served as a Member of Parliament for Morpeth from 1774-89, through the influence of his wife's family. He sold his estate Erle Stoke, in Wiltshire, and purchased Cams Hall, in Hampshire. On 16 February 1769, he married Lady Elizabeth Howard, 5th daughter of Henry Howard, Earl of Carlisle. They had four sons and a daughter. John Delmé succeeded his father in the estate of Cams Hall. Around 1777-79, Delmé commissioned Sir Joshua Reynolds to paint a portrait, now in the NGA, of his wife and two oldest children.
Burke, Sir Bernard. A Genealogical and Heraldic History of the Landed Gentry of Great Britain & Ireland. 2 vols. 8th ed. London, 1894: 1: 500.