Named after Admiral Lord Exmouth, the victor of the Battle of Algiers in 1816, H.M.S. Exmouth was begun as a pure sailing ship in 1841 but finally launched in 1854 by which time she had been fitted with a screw propeller. A large Second Rate mounting 90 guns, she was measured at 3,109 tons and was 243½ feet in length with a 60 foot beam. Capable of 9 knots under steam, her first commission was to the Baltic during the war with Russia in 1855 but she returned to Portsmouth at the end of that year where she remained until sent to join the Mediterranean Fleet in 1859. Based at Malta, she stayed there until called home late in 1861 after which she was laid up at Devonport until 1876 when she was put to work as a training ship for "poor boys of the metropolis" (i.e. London). Moored in the Thames off Grays, Essex, she fulfilled this role for almost thirty years until scrapped in 1905 when she was found to be beyond economic repair.
It seems likely that this portrait was commissioned by Captain Paynter, her commander in the Mediterranean and the officer who brought her home from her final sea-going commission.