The surving crew faced court-martial.

 

(With due consideration of Wikipedia's reliability.) There is an interesting story of HMS Alacrity and her loss to the French.

HMS Alacrity was a Cruizer-class brig-sloop built by William Rowe at Newcastle and launched in 1806. She served in the Baltic and was at the capture of Copenhagen in 1807. She captured a large privateer before herself falling victim to a French man-of-war in 1811 in an action in which her captain failed to distinguish himself. She then served in the French navy until she was broken up in 1822.

A newspaper account of the capture reported that when Palmer and Alacrity had sighted Abeille, Palmer had sent three boats to cut her out. However, the French had captured the cutting-out party. They then took the boats in tow and sailed towards Alacrity with English colours hoisted over the French, a ruse suggesting that the cutting-out party had succeeded in their mission. The French ran alongside Alacrity and carried her by boarding. Within a month of the battle Palmer died of tetanus from his otherwise minor wound. The court-martial of the survivors on 30 May 1814 attributed the loss to a lack of leadership. It acquitted all the survivors and commended the boatswain, James Flaxman, who had remained on deck though wounded and had attempted to rally the crew to Alacrity's defence.

As is British naval tradition, the Alacrity in name saw further service.

HMS Alacrity (F174) was active during the Falklands War of 1982, where she sank a supply ship, survived Exocet-missile attacks and rescued men from the Atlantic Conveyor. She was transferred to Pakistan on 1 March 1994 and renamed PNS Badr.

There does not appear to be an active Alacrity in Royal Navy service.