Britain's post-treaty heavy-cruiser studies

Did the Royal Navy consider large post-treaty heavy cruisers rather than simply more County-class ships?

Yes; it studied 9.2-inch cruisers, but World War II began before they could be built.

Britain considered heavy cruisers beyond the treaty limits, with 9.2-inch guns. The Admiral Hipper class provides the comparison with a design already exceeding the treaty framework in practice. World War II interrupted the British plans before construction. A later war, around 1942, might have given such ships time to be built.