An unrestricted British fast battleship and the gun-size race

What might Britain build if it pursued the strongest possible fast battleship, and how would other navies respond?

Britain could build a roughly 35,000-40,000-ton, 28-knot ship with 16.5-inch guns. German affordability and American gun-size politics could shape the responses.

The hypothetical British design combines roughly 35,000-40,000 tons, 28 knots and 16.5-inch guns. Its exact battery is unclear in the discussion. Germany would struggle to pay for a competitive response. American decisions would also face the politics of appearing to have smaller guns. A British 16.5-inch/45 and American 16-inch/50 could be broadly comparable, yet nominal calibre would be easier to communicate to Congress. American politicians could consequently demand an 18-inch gun. More battleship spending would compete with needed cruisers and destroyers.