Under Captain Richard Bickerton, "Fortitude" served in the English Channel. In April 1781 she participated in the second relief of Gibraltar. In May 1781, during the Fourth Anglo–Dutch War, Vice-Admiral Hyde Parker's shifted his flag from to "Fortitude". On 5 August, "Fortitude" fought in the Battle of Dogger Bank as Parker's flagship. After a desperate, bloody battle in which neither combatant gained any advantage, both sides drew off.