Lets assume that instead of FDR we get a fascist-sympathetic, it not outright fascist, administration in the USA. Instead of the Atlantic Charter IOTL there is an agreement with Germany to dismantle what is left of the British Empire.
The USA is still hostile to Japan, and vice versa, so for lack of alternatives the UK and Japan have to draw close to each other, and close to the USSR since Barbarossa still happens.
How does that war go? My first thought is the Axis wins, but there may be valid counter-arguments.
Well, for starters China is now firmly in the German-American camp, since any British-Japanese rapprochement means London has to accept their ally's long standing interests in the country (Possibly splitting influence within the country on a mutual pro-Imperial/protectionist policy and search for captive markets and raw materials to bolster their faltering domestic industry). The Nationalists then are going to be receiving Nazi-American aid during the critical pre-war years in terms of technical expertise, investment, ect. that will make them a more (if not exactly overpowering) conventional combatent with a more robust economy in its showdown with the Imperials, likely having incorperated the warlords better and having effectively purged the Communists who will have fled to the Soviet Union. This will turn the Asian front into a pretty solid resource sink, especially since the British ability to send meaningful support would be limited without L-L, American loans, and the need to bolster defences elsewhere against American agression and defend the Home Isles from the Germans. Still, the Pacific theature is rather rosey from a naval point of veiw: the Dutch East Indies is likely to collaberate with the Japanese with the dutch government-in-exile under British protection and American positions in the Phillipenes hopelessly exposed.
However, the Imperials are quickly going to run into one huge problem: The economy, specifically in the form of calories. Once Barbarossa snatches up the good Soviet farmland, they're all massively calorie-deficet homelands whose merchant shipping is now at deep risk, sucked into the need to sustain the war effort, or otherwise indisposed and who's best markets are now either under hostile control or highly vulnerable to Axis pressure, invasion, or indication. This is all assuming they could scrape together the cash to pay for what they'd need on the international market, which they can't, and rationing can only go so far: particularly when mechanized agriculture is also going to be taking a huge knock from lack of civilian fuel. Rather quickly, they'll find they can't keep up a good homefront quality of life unlike the American-German Axis, and will need guns over butter in order to hold out, which I imagine will very quickly lead to a collapse in the British war party or at the very least a breakdown in the solidarity of the Empire, with South Africa and India being the first to jump ship if England tries to lean on them too hard and Canada either not declaring war at all (Essentially declaring independence at the start of the war, excersising its independent forgien policy) or quickly falling to the Americans. Its only a matter of time before the same fate befalls the Soviets, and Britain and Japan find they can't keep the underlying civilian economy needed to support a Total War running on what fumes they have.