In the War of 1812 he commanded British naval forces during the Burning of Washington.

In 1815 he was charged with escorting the deposed French emperor Napoleon into exile and British captivity on the Atlantic island of Saint Helena.

Cockburn is shown wearing the dress uniform of a vice admiral and the star Order of the Bath.

He wears the sword presented to him by Horatio Nelson in 1797 while his hand rests on a map of Cockburn Land on Baffin Island.

The painting is in the collection of the National Maritime Museum in Greenwich.