How reliably would the uk be able to pull troops from India?How long is the Empire going to keep fighting?
My first thought was supply the Allies but otherwise stay out, but that assumes that the Allies can keep fighting. At historic tempos the UK is out of warm bodies by 1945. Of course the Allies will be slowing down into siege mode in this scenario, but they can't keep fighting forever. There goes the US's proxie.
At this point you have to wait for the internal contradictions of the Axis powers to tear them apart and provide a new opening.