Washington and London cruiser limits differed

Could Britain accept K3 restrictions in exchange for a larger cruiser allowance?

Not under the historical Washington framework, which had no aggregate cruiser allowance to trade; that mechanism came later at London.

The Washington system limited the size and armament of individual cruisers but did not impose a cumulative cruiser allowance. Britain therefore had no aggregate tonnage concession to receive in exchange for accepting restrictions on K3. Fleet-wide cruiser limits arrived with the London treaty. There, Britain sought to protect its need for numerous light cruisers against rivals concentrating tonnage in large 8-inch-gunned ships.