HMS Alcmene was a 32-gun Alcmene-class fifth rate of the Royal Navy. This frigate served during the French Revolutionary and Napoleonic Wars under the command of several notable officers. Alcmene was active in several theatres of the war, spending most of her time cruising in search of enemy vessels or privateers, and escorting convoys. She fought at the Battle of Copenhagen in 1801 and served in the blockade of the French coasts during the later Napoleonic Wars until she was wrecked on the French coast in 1809.

The Battle of Copenhagen of 1801, also known as the First Battle of Copenhagen to distinguish it from the Second Battle of Copenhagen in 1807, was a naval battle in which a British fleet fought and defeated a smaller force of the Dano-Norwegian Navy anchored near Copenhagen on 2 April 1801. The battle came about over British fears that the powerful Danish fleet would ally with France, and a breakdown in diplomatic communications on both sides.