At the start of the French Revolutionary Wars in 1793 Sutton was promoted to post captain and took command of first the frigate HMS "Romulus" and then the ship of the line HMS "Egmont", which was attached to the Mediterranean Fleet. In 1795 "Egmont" fought at the battles of Genoa and the Hyères Islands, suffering casualties on the latter when a cannon burst. The following year he served on an operation to attack a French squadron in the harbour of Tunis and Sutton was then particularly tasked with the orderly evacuation of the British base on Corsica following the Spanish entry into the war on the French side.