There seems to be a belief that the war against Japan is a resource hog, and that for the British it will become something that they are prepared to leave to the Americans. Churchill while not a fool by any measure, and well understanding that the war against Germany is and has to be the main priority. Will for reasons that would to modern eyes seem foolish, Imperial prestige, not want to allow the British campaign to be seen to be anything other than full hearted.
It should be remembered that Japan is fighting three wars, one that has been ongoing since before 1937 against China. And it is this war that occupies the majority of her ground troops, and a large portion of her Airforce. Nor can see withdraw to many forces from this conflict without the Chinese taking advantage of this. No matter how ineffectual Chiang was, if the Japanese take the pressure off him, he will attack, and they will find themselves losing, not something the army is going to allow.
Then there is the predominately naval campaign in the Pacific, against the Americans, and the mixed campaign in South East Asia against the British. ITTL, both of these campaigns play to the respective nation’s strengths, and against the Japanese. Who have entered a game in which they can not win, or can they afford to play.
It should be remembered that with the demise of both the German and Italian fleets, courtesy of the FAA, there is only one place in the world that major surface naval units can be deployed to any significant effect. That is in the war against Japan, and both the RN and USN, are going to want to have their chance to play in this area. After all, the only other option is convoy duty, not something that the professional officers relish, or see as providing a career enhancing addition to their CV.
For the Americans, the Pacific campaign once they have ramped up their war industries is a low personnel, high material cost effort. And that is their preferred way of fighting; America has ever since the Civil War preferred to spend money more than lives. (This is not a criticism, just an observation.) The Pacific war was up until the invasions of the Philippines and Okinawa, one that required few troops in combat in comparison to the number in support. And where American logistics, and its ability to provide an endless stream of equipment and stores was a deciding factor.
ITTL, the British too, are free to fight in a way they prefer, and also have a logistical advantage over the Japanese that they didn’t in OTL. With both Singapore and Rangoon available, they can supply their forces in a way they were not abler to IOTL. Other than in the New Guinea campaign, no other front had as difficult supply chain as that in OTL Burma. Slim was always fighting on the edge of his logistical ability, and it was logistics that dominated all his efforts.
Now both he and Alex, are to a major extent free of those worries, both have a major port at there conveyance, and can supply their respective forces far easier than Slim could IOTL. Nor are troop numbers a worry, India and local recruiting are more than enough to provide the men they need. As for equipment, without the prolonged campaign in the Middle East, and better results in the Atlantic war, more will be available than was. The war in the Far East isn’t highly mercerised, nor is the fighting high intensity in the way it was in Europe. Local conditions preclude mass tank armies, and the use of massed artillery.
Britain will conduct a major campaign as it did IOTL, and this will not to any great extent distract from the efforts in Europe.