A 74-gun, third-rate ship of the line, she was built by Randalls of Rotherhithe and launched on the Thames in 1798. When first commissioned she was a part of the blockade off the coast of France and was commanded by Captain William Brown. However, because Captain Brown had been called as a witness at a court martial, the ship sailed from Plymouth along with HMS Victory and HMS Thunderer on 18 September 1805 under the captaincy of First Lieutenant John Pilford.
At Trafalgar, HMS Ajax was seventh in line in Admiral Lord Nelson’s column and she fired on both the French ship Bucentaure (74 guns) and the Spanish ship Santissima Trinidad (136 guns) before assisting HMS Orion in forcing the surrender of the French 74-gun ship Intrepide, losing just 2 of her crew with a further 9 injured. During the storm that followed the battle, HMS Ajax rescued many seamen from ships in danger of sinking.
In 1807, she was serving in the Dardanelles as part of a squadron under Admiral Sir John Duckworth when fire broke out in the cockpit late one evening. As the fire burned out of control, passengers and crew were forced to take to the water. Although 380 people were rescued, 250 lost their lives that night including many of the crewmen who had been at Trafalgar.
William Sewell joined HMS Ajax on 1 March 1805 as a Landsman aged 20, stating his place of birth as Whitehaven, Cumberland. It is likely that he survived Trafalgar and was still with the ship in 1807 when it was destroyed.