Britain experimented with battleship guns in anti-aircraft defense

Did the Royal Navy consider anti-aircraft shells for its 14- and 15-inch guns?

Yes; Britain tested and deployed very heavy anti-aircraft fire, and wartime reports even credit Rodney's 16-inch guns with an aircraft kill.

The Royal Navy did investigate anti-aircraft ammunition and use for its largest guns. A 15-inch anti-aircraft installation produced an enormous burst and created an area that German bombers preferred to avoid. A later follow-up notes reports that an aircraft attacking Rodney folded up in midair after a 16-inch salvo. These weapons were inefficient substitutes for normal anti-aircraft batteries, but their shock effect was real enough to influence behavior. Heavy-gun fire occupied an unusual edge of British air-defense doctrine.