During his long service, Otway saw action across Europe and in North America and was rewarded in his retirement with a knighthood, baronetcy, and position as a courtier within the Royal Household.

The eruption of the French Revolutionary Wars in 1793 brought Otway back to Europe as a lieutenant on the second-rate ship of the line HMS Impregnable with the Channel Fleet.

Otway distinguished himself in the action by going aloft despite the heavy fire of the French fleet to repair the damaged fore topsail yard and thus allow Impregnable to engage the enemy closer.

[1] His exploits during this period included destroying, on two separate occasions, the sloops La Belle Créole and Courier National which were on passage to Guadeloupe with orders to massacre the French Royalist population there.

He later supported insurgencies in French held Grenada and St. Vincent and also raided La Guayra in Venezuela in an unsuccessful effort to capture HMS Hermione, whose crew had mutinied, murdered their captain, Hugh Pigot, and turned her over to the Spanish.

[1] Admiral Thomas Ussher, who served under Otway during this period, later reported "that no captain was more attentive to the comfort of his officers and men and that there was so much method in his manner of carrying on the service that, though in a constant state of activity, they had as much leisure as any other ship's company."

Otway was still at this post when Parker lead a fleet to the Baltic Sea to engage the League of Armed Neutrality which threatened Britain's trade routes in the region and he was an important contributor to the tactical planning of the Battle of Copenhagen.

[1] By 1804 he was sufficiently recovered to take command of HMS Montagu off Brest under Admiral William Cornwallis and whilst on this duty he participated in a brief artillery duel with the Alexandre during the French attempt to break the blockade in August 1805.