The ship was ordered on 24 April 1773 as an "Intrepid"-class ship of the line of 64 guns. The lead ship of the class, , had entered service in 1771 and proved satisfactory in sea trials, so the Royal Navy increased their order from four to fifteen ships. "Anson" was part of the expanded order, named after George Anson, 1st Baron Anson, the victorious admiral of the First Battle of Cape Finisterre (1747).