Choosing a post-Falklands big-gun caliber

In a timeline where Britain keeps its big-gun ships and builds a new post-Falklands command ship, should the weapon be 14, 15, 16, or 18 inches?

A British-only project would probably use existing 14- or 15-inch support capacity, most plausibly standardizing on 15 inches; a joint American project could justify a new 16-inch gun.

Keeping Vanguard and the King George V class in service would preserve facilities and stockpiles for 15- and 14-inch weapons. A British-only project would choose between those existing systems instead of reopening an 18-inch path. If Vanguard remains, a 15-inch weapon would let Britain retire the 14-inch stock and support one domestic caliber. A joint American program changes the economics enough to make a new 16-inch weapon plausible.