Britain's 16.5-inch gun as the next design step

Was the proposed British 16.5-inch gun a two-step enlargement of the 13.5-inch gun?

No. The 15-inch weapon adapted the 13.5-inch design to save time, while the 16.5-inch/45 belonged to the next development program.

Britain accelerated the 15-inch gun by adapting the 13.5-inch design, producing a 42-calibre weapon from work on a 45-calibre gun. The proposed 16.5-inch gun belonged to a separate development program that was proceeding alongside that work. It is described here as a 16.5-inch/45 design, rather than a second enlargement of the 13.5-inch weapon or a 50-calibre gun. In the German 15-inch-gun counterfactual, that program supplies the quickest proposed British response.