In October 1710 he led a convoy to Smyrna aboard HMS Dreadnought, but his Whig politics made it impossible to gain a further command on his return, and he languished on half-pay for some years.

His first task was to open negotiations with Ismail Ibn Sharif, emperor of Morocco to "demand satisfaction for the depredations of the Salé corsairs and procure the release of all His Majesty's subjects now captive in Barbary."

[2] Cornwall was promoted to vice admiral in March 1718, and became second-in-command to George Byng on the latter's arrival in the Mediterranean in June of that year, hoisting his flag aboard HMS Shrewsbury.

Cruising with a combined force of nineteen ships of the line, two frigates and a galley off Syracuse they attacked a Spanish fleet in the battle of Cape Passaro on 31 July 1718.

Cornwall's part of the fleet was charged with the pursuit of the Marquis De Mari, who led a force of six ships of the line, nine frigates and a number of smaller vessels aboard his flagship El Real.

[10] After the battle, Cornwall transferred his flag back to HMS Argyll and convoyed the captured Spanish prizes to Port Mahon, from where he set sail for England.

[11] Cornwall's career had been illustrious without being spectacular, as John Charnock put it: "We have at least a very extraordinary, if not unequalled instance in this gentleman, of its being possible for an officer to serve, with the most irreproachable character, and to attain a very high rank in the service, without ever having it in his power to increase his reputation, by any of those brilliant exploits which fortune throws in the way of her greater favourites.