While this is a particularly devastating event and a good portion of the Pacific Fleet has been crippled HM Government is working with the Hawaiian Government to get the situation under control. The shipyards, dry docks and oil farms have not been touched.
The main units of the Royal Hawaiian Navy are still intact and have been withcalled from their exercises down in Tonga, tho its likely they may be moved to Fiji in order to support the Royal Australasian Navy.
However, the six battleships lost, while tragic, where not the first line of battleships that the navy has. HMS Resolution and her sistership HMS Resistance, with their 8x15in were the core of the fleet. The four other ships were members of the Iron Duke and King George V classes and haven't been modernized since just after the Great War.
The Pacific Battlecruiser Squadron in Esquimaux, British Columbia, is still in full strength, tho they may be dispatched to Hawaii when its deemed safe. The Royal Canadian Navy has been placed on alert, but its unlikely that the Japanese will attack further east that Hawaii.
It would have been far worse if any members of the giant St. George, Nelson, Queen Victoria class battleships - with their 9-18in guns, were lost, but those very infrequently are dispatched east of Suez.
IIRC the HMAS Dominion, HMAS Victoria, HMAS New South Wales, with their 9-16in guns, are currently the largest battleships of the British Empire in the Pacific. The Royal Hawaiian Navy only has their old battleships, HMS King Kalakaua and Queen Liliuokalani, with their 10-15in guns - tho they do possess the aircraft carriers Mauna Kea, Mauna Loa and Iolani which may serve as the new core for any further fleet actions.