A British counterpart to the Alaska class

Did Britain consider something like the U.S. Alaska class?

Yes. British 9.2-inch cruiser studies are the closest analogue, emphasizing a higher rate of fire rather than Alaska's larger gun calibre.

Britain considered large cruisers armed with 9.2-inch guns, including a twelve-gun arrangement. Those studies are the closest British counterpart to the Alaska class rather than a direct copy. The calibre choice resembles the six- versus eight-inch cruiser debate because broadly similar reach can be paired with different shell weights and rates of fire. A British design could therefore emphasize a denser volume of fire instead of simply matching Alaska's larger guns.