I'm sketching out a plan for a TL featuring a Pacific War without the USA and a British Empire that's free to expend it's forces completely on Japan.
Which force was stronger? Which force would win?
It hugely depends on when. The IJN of 1942 was a far different beast than the one of 1936, for example. In 1942, assuming butterfly nets ensure naval development is largely the same, I think Japan could win a short war. Longer wars, as well as earlier or later ones, may well favor the UK.
You say that the US is not in the war, but what are they actually doing? Are they true neutrals? Do they sell oil to Japan? Do they sell weapons to the UK? Are they willing to sell anything to everyone, or nothing to anyone?
Finally, why did this war start? How serious are the two sides? In many scenarios, the UK could win by enforcing a blockade, or using submarine interdiction, but are they willing to fight a long war, a la the Pacific War? Or, on the other hand, are both sides hoping for a quick victory, and a big naval victory here or there will decide the issue? Are they going to war with the navies they have? In certain time periods, that would favor Japan, but if this is a years-long conflict in which the Brits can build up their forces over time, that obviously favors them.