What actually happened was that the Axis waited for UK to parlay on the public Offer of Me, Eurasia Land Mass, You, the blue briney. They were just as surprised as UK Joe Public that Parliament applauded and agreed no surrender, fight on the beaches. With What/Who?
If you are of the view of L Halifax (Foreign Secretary, 6/40) - leave Germany to bash the Bolshies, then clean up World Markets denied to exhausted Axis (=Isolationism), then: Barbarossa Spring 1941, all over by Christmas. This forum today in the German language.
Or, per Arjen::
Somewhere around top of the Persian Gulf Japan links up with the European Axis, so owning Eurasia, owning most fuel in the Eastern Hemisphere and with Naval Power sufficient to isolate US (who don't care) and UK (who do), so a tense time of Trade Protected by Naval Power (RN bunkered in Trinidad). With no casus belli, that could go on forever, US owning Western Hemisphere Trade, UK owning Oz/Sub-Sahara, because young men would have no imperative to fix bayonets to try to change things. There's a limit to the willingness of families to die for obscure causes.
This outcome did not happen for 3 reasons: FDR cutting Japan from NEI oil, so Pearl bringing US in to the Eastern War;
Hitler's interpretation of his Japan Agreement as requiring him to Declare on US, so bringing US into European Defence;
and the Bomb coming to pass with the Good, not the Bad Guys.
(Howzat! I liked that).