Between 1901 and 1910 Japan WAS Britain's best ally.
You can kill off the Triple Entente, have it remain a couple of separate billateral agreements.
Or you can have Japan not do so well in the Russo-Japanese War - you don't want them to lose, but maybe Rozhestvensky dies enroute and someone with more faith takes over the Russian fleet and fights through to Vladivostock. With a fleet in being, and with the war in Manchuria stalemating because of running out of supplies, Japan won't be seen as increasingly the Big Bad.
It may seem counter-intuitive to retard Japan's advancement thus, but you need to avoid a situation where they emerge as powerful enough to make demands on China that everyone's backs up
In the above you would need to avoid the First World War, but if you decided to have it then ignore the above and try perhaps all you need to do is have the Dardanelles succeed, Russia stand tall and remain strong in the East. End the war in say 1916 and Japan has not emerged as the threatening power as per OTL
Best Regards
Grey Wolf