Painting on the wall behind Harrison Ford in the Oval Office

I recently watched this film and noticed that in one of the final scenes, when Harrison Ford was with the President in the Oval Office, mounted on the wall behind Harrison Ford was a large painting of a man in uniform and of some age. I think this was a full length portrait of Admiral Sir George Cockburn standing in front of the White House which he had ordered to be burnt down. The scene behind him is of the White House in flames. Does anyone know if this is correct? The reason I ask is that many years ago, as a relative of the Admiral (my great-grandmother was a Cockburn), I made a pilgrimage to the Greenwich Maritime Museum in Greenwich, London to see this painting. The Museum tells me that this painting was never loaned out to a film company but somebody, somewhere must know something about this and it's now become an obsession to find out if what I saw in that scene was, in fact, the painting of my forebear.