How Britain might choose naval gun calibers without treaties

Would Britain have retained the proposed capital-ship, cruiser and destroyer gun calibres without the interwar treaties?

Broadly, but the destroyer caliber was still contested and could have ranged from 4 inches to 5.5 inches depending on fleet design choices.

The proposed sequence of capital-ship, cruiser and destroyer calibres broadly fits British thinking, but the destroyer gun was still undecided. A 4.7-inch weapon was a plausible outcome, with 4-inch and 5.5-inch alternatives considered at different points. A 5-inch gun also had a strong case. A substantial force of 6-inch light cruisers could favour a lighter destroyer weapon, while a longer-barrelled 4.7-inch gun offered another possible compromise.