In Vestal he made an aborted journey to China before serving on the East Indies Station where he transferred to HMS Phoenix and fought in the Battle of Tellicherry and the Third Anglo-Mysore War in 1791 and 1792.

In 1797, he successfully combated the Nore mutiny in Circe before fighting in the Battle of Camperdown where he personally captured the Dutch admiral Jan Willem de Winter.

[9][14] Here he left the frigate, and joined instead the 74-gun ship of the line HMS Alexander on 28 December, serving in Admiral Lord Howe's Channel Fleet.

[16][22][23] On 4 August of the same year, he was promoted to lieutenant and sent to join the 28-gun frigate HMS Circe in Admiral Adam Duncan's North Sea Fleet.

Richardson and his captain, Peter Halkett, sat back-to-back on the quarterdeck armed with pistols and carbines and succeeded in keeping control of Circe, for which they were thanked by the Admiralty.

[27] Circe was subsequently employed in the squadron of Captain Henry Trollope to patrol off the Texel, and was then present at Duncan's Battle of Camperdown on 11 October, where she served as a repeating frigate.

[Note 4] As the battle came to a close the Dutch admiral Jan Willem de Winter's flagship Vrijheid had been dismasted and was lying silent.

[9][29] In 1799 Kent was sent to support the Anglo-Russian invasion of Holland and Richardson was sent ashore with a contingent of seamen, with which he controlled a gun battery attached to the army of Lieutenant-General Sir Ralph Abercromby.

[9][35] Richardson was by this point first lieutenant of Kent, and he was given responsibility for landing some of Abercromby's army when they arrived, which took place at the Battle of Abukir on 8 March 1801.

Richardson was rewarded by the commander-in-chief in the Leeward Islands, Commodore Sir Samuel Hood, with the acting command of his flagship, the 74-gun ship of the line HMS Centaur, on 6 July.

[9][49] Richardson returned to England with Hood in March 1805 and soon after left the ship, going on leave to Westmorland where he purchased a small cottage and thirty-six acres (fifteen hectares) of land and visited his relative, Sir Francis.

[9][45] They chased Willaumez to Brazil and the Leeward Islands but failed to catch him, and Richardson subsequently served in Caesar in the blockading force off Rochefort.

Then on 11 April the squadron participated in the Battle of the Basque Roads, where fireships assisted in destroying four French ships of the line that had been part of the same fleet as the frigates at Les Sables-d'Olonne.

[9] He went ashore on 30 July in command of a brigade of eighty seamen, and a day later the gun boats of Strachan's squadron attacked the Dutch town of Camvere.

When the ships were forced to halt their bombardment because of a change in the wind towards the end of the day, Richardson set up a battery of incendiary rockets on top of a dyke and opened fire on the defensive positions around the town.

[56][57][58][59] In his report on the action, Strachan gave the credit for the fall of the town to Richardson and his rocket initiative, the new weapon having scared the garrison into capitulation.

[60] The 519 Dutch soldiers from Camvere were taken as prisoners of war in the morning of 1 August, and the British force then moved on to attack the nearby fortification of Fort Rammekens [nl], which controlled the waters of the West Scheldt.

[61] On 12 August the expedition attacked Flushing, the only Dutch strongpoint remaining on Walcheren, and Richardson had his men man a battery of six 24-pounder cannon.

[Note 6] In the early morning of 14 August Richardson finished mounting the guns of his battery, 600 yards from the town, and in two hours destroyed all the Dutch cannon facing him.

Richardson then attacked her as she attempted to make sail to defend herself, and through excellent seamanship he managed to force Pluvier aground at Royan.

Despite the French warship lying under the guns of a friendly battery, he then succeeded in burning the vessel where it lay with his newly returned small boats.

[69] After this Richardson continued in a successful run of prizetaking in Semiramis; at the beginning of 1812 he was sent to serve on the Irish Station, where he captured the French 14-gun privateer Grand Jean Bart on 29 February.

[9][56] Leander was the flagship of Rear-Admiral Sir Henry Blackwood, who had been Richardson's captain in Penelope and had now been given command of the East Indies Station.

[74] Upon arriving at Canton his crew created a severe diplomatic incident after firing on a group attacking Topaze's watering party on Lintin Island and killing two locals.

On 14 October, with his health described as being in a "very dangerous state" by biographer John Marshall, he was invalided home via the Cape of Good Hope, also suffering from a severe fever.

[9][71][78] This was Richardson's last active service in the Royal Navy, but he continued to be rewarded and promoted in retirement, becoming a rear-admiral on 10 January 1837, a Knight Commander of the Order of the Bath on 29 June 1841, and a vice-admiral on 17 December 1847.

[Note 9][56] In the same year he received the Naval General Service Medal with clasps for the Glorious First of June, Camperdown, Egypt, and the Basque Roads.