Why can't the Soviets, with the commitment of heavy amounts of labor and at least for 1940 and 1941*, seize the middle East, intimidate Turkey into at least transit rights, if not a communist coup, and throw India into revolt? The UK will be trying to avoid having the BEF encircled in France and struggling to hold North Africa.
- As I mentioned, you likely have a far stronger Indian Army fighting with the British, but there very likely will arise an issue as to who among the "Axis" occupies what parts of the Middle East; Hitler would prefer Stalin keep to Iran and move into India for example.
- Hitler is not going to let Stalin force the Turks hands, considering it would serve as a major threat to his interests in the Balkans; even forcing transit rights, unless they are made jointly with Nazi Germany, would in Hitler's mind serve to throw Turkey entirely into the Soviet orbit.
- Factions only slightly more significant than those found by the Axis in OTL would exist; while there was a lot of support for Socialism, I don't believe that would translate into support for the Soviet Union if the British are willing to "pay a price".