I think this must be Stroomloodsvartuig 4, also called Pilot Boat 4, a Dutch/British (apparently) cutter that had the misfortune to be chanced upon by three German destroyers south of Cornwall on the night of the 28th. The German destroyers Lody, Galster and Beitzen sailed from Brest in the early evening and came across two tugs and a lighter, sinking the lighter and one tug. The then moved west and came across Pilot Boat 4 which was sailing from Plymouth to Falmouth and, after firing some 50 to 60 rounds, eventually sank her. Her survivors were picked up by HMS Jackal the next morning.
The action is better known for what happened next. HMS Javelin, Jupiter, Kashmir, Jackal and Jersey intercepted the destroyers and a close engagement followed. Javelin had her entire bow blown off by a German torpedo, which was unfortunate for the captain who had just had HMS Kelly put into drydock after she'd been badly damaged by a torpedo. Still, it doesn't seem to have done Lord Louis Mountbatten's career much harm...
The action is fairly well described in German Destroyers of World War II by M J Whitley, from whom I've sourced the above. Googling HMS Javelin and 29 November should tell you a bit more. Pilot Boat 4 will probably only be a footnote though I'm afraid. All I can say is that Whitley describes her as a cutter, and that the combined tonnage of both her and the lighter was only 424 tons (the Germans claimed 1,000 each!). Admiralty records in The National Archives will have more I'm sure, probably in the Plymouth Command books. At a guess she was a Dutch vessel taken on for war work, either as a British crewed merchant ship, or possibly an emergency picket boat of some sort.
Hope this helps,