This pencil and ink drawing is described on pages 17-20, 197, 146-8, of the 'The Nelson Portraits', by Richard Walker, although the information says that it hangs at the Royal Naval School, Holbrook (as it then was).
The expert on the show was correct, in that it is by Henry Etheridge (and drawn in 1797), but appears to be a little out in saying that it belonged to Earl St Vincent. The information in Walker's book says that it was commissioned by Sir Henry Engerfield, brother in law of Richard Bulkley (an old comrade of Nelson), and on his death it was sold at Christie's, on 8th March 1823, to Sir Everard Home. He was the son of Vice Admiral Sir George Home, and he bequeathed it to the Royal Naval School in 1854.
In passing, it is unusual to see Nelson minus his decorations – apart from his medal for St Vincent, and the sash of the Order of the Bath. It is rather confusing though to show a different portrait of Nelson further down.
Oh, and the head boy is no relation – so far as I know!
