Why British big-gun studies gravitated toward 16.5 inches

Did the Royal Navy ever consider a naval gun around 16.25 inches?

Yes, but British studies above 15 inches more often concentrated on a 16.5-inch calibre.

A 16.25-inch calibre appeared in Royal Navy thinking at one point, but the service returned more often to 16.5-inch weapons. British studies moving beyond 15 inches did not always follow the round-number progression familiar from completed American or Japanese guns. Design studies can cluster around calibres that never become standard fleet armament.