She was launched at Whitby in 1799 under the plain name New Grove and spent her first years hauling cargo between London and Jamaica, later carrying goods to Suriname under a master named Barclay. It was ordinary commercial work, the backbone of an empire that ran on ships like her. In October 1803, with Britain again at war with Napoleon's France, the Admiralty bought her. At Woolwich Dockyard, through the winter into March 1804, shipwrights rebuilt the trader into a bomb-vessel, reinforcing her hull to absorb the recoil of her mortars. Commander Arthur Farquhar took command in December 1803 and sailed her for the Mediterranean, where the Navy was locked in the long, grinding blockade of the French fleet.

By July 1804 Acheron was one of the ships bottling up the French in Toulon, a monotonous, weather-beaten duty that Nelson's captains knew intimately. Early that August a storm blew the British squadron off station, and the French admiral Latouche Treville seized the gap to take his ships out for a training run, though he made no attempt at the grander voyage Napoleon wanted; sick already, he died within days. The blockade offered small rewards between long stretches of tedium. In November Acheron took the prize Adamo and shared in a string of captures made by Nelson's fleet. It was unglamorous, essential work, and it kept the French bottled where they could do no harm.

In January 1805 Acheron was ordered to a different task: shepherding merchant ships home. Alongside the sloop Arrow, under Captain Richard Budd Vincent, she escorted a convoy of nearly thirty merchantmen out of Malta toward England. Bad weather off Spain scattered the ships into two groups. Sighted off Cape Caxine on the third of February, the two powerful French frigates, Hortense and Incorruptible, gave chase and fell upon the convoy near Cape Palos on the fourth. Against frigates, a bomb-vessel and a sloop were badly overmatched, yet Arrow and Acheron turned to fight rather than flee. Their resistance bought precious time. Arrow's hold filled with water, four of her guns were torn from their mountings, and she took heavy casualties before she struck and rolled onto her beam ends, sinking as French boats pulled her survivors from the sea. Acheron, battered beyond saving, was set ablaze by her captors.

The two small ships had done exactly what escorts are meant to do. While the frigates were occupied, the great majority of the convoy slipped away; the French managed to seize only three vessels, which they scuttled. Farquhar and his men were carried into Malaga and exchanged before long, and at the court martial that automatically followed the loss of any ship, held in Palma Bay off Sardinia, he and his crew were honorably acquitted. Farquhar was promoted to post captain for his bravery. Captain Vincent of the Arrow fared harder, held prisoner in Cartagena for nearly three months until Nelson arranged an exchange. Decades later, in 1847, the Admiralty struck the Naval General Service Medal for the action. By then only a single survivor from Acheron lived to claim the clasp engraved with her name and the date.