Charles Elphinstone Fleeming (18 June 1774 – 30 October 1840) was a British officer of the Royal Navy who served during the French Revolutionary and Napoleonic Wars.

Combining his naval career with periods of political activity he took part in only one major fleet operation, the Battle of Cape Finisterre in 1805, but spent several years as a Member of Parliament.

Connected by birth to a major noble landowning family several of his children went on to inherit or marry into titles and rank in the British peerage.

[1][2] He moved aboard the 26-gun HMS Tartar on 7 October 1795 and commanded her until her loss in 1797 while attempting to cut some French merchantmen out under the batteries at Puerto Plata, on Saint-Domingue.

[1][3] He was then appointed to the 50-gun HMS Diomede in March 1798 which he commanded initially in the North Sea, but departing for the Cape of Good Hope on 6 December that year.

After the battle, Admiral Robert Calder requested a court-martial to review his decision not to pursue the enemy fleet after the engagement.

[1][13] He had been re-elected three times as MP for Stirlingshire before his naval career intervened, but returned to politics during his retirement from active service, regaining the seat in 1832 and holding it until 1835.

Fleeming married 16-year-old Doña Cataline Paulina Alesandro de Jiminez in June 1816 in the Cathedral of Santa Cruz in Cadiz; he was 42.

[18] He succeeded Sir Thomas Hardy as Governor of Greenwich Hospital in September 1839, holding the position until his death from influenza at Leamington on 30 October 1840 at the age of 66.