Search engines can be funny things. I had been googling just "Kempthorne" with no result.

Of course, I'm not going to stick my neck out and say that 23/24th Feruary was in fact composed in honour of J. Kempthorne's battle as it wasn't a unique event. The same Wiki article says that his son Morgan was killed fighting alone against seven Algerian ships, and there was a ballad written in 1590 -

"A Dittye of the fight upon the seas the 4 of June last in the Straytes of Jubraltare between the 'George' and the 'Thomas Bonaventure', and viij Gallies with three Freggates" [Records of Stationers' company]