British commitments to the Middle East would be stepped up with aid from the United States, and also present problems for Turkey. The Kurds would likely establish as they did historically rebel groups in Turkey and Iraq to split those regions off into their new Republic. In the case of Iraq, this also threatens the Mosul regions, which would be considered vital to Allied interests.
As for Iran, sections of Northern Iran would likely be detached in the West for the formation of the Kurdish People's Republic, and maybe annexations into the Azeri SSR. Basically, the situation develops along a similar path as has occurred between the Two Korea's, though there would not be a war (The Soviet Union would not wish to lose access to the Southern Caspian Resource Zone), and the North would be more economically viable (for the same reason).
The problem here is that the Soviet Union becomes popular among the minorities within the Middle East, whereas due to its support of the said minorities, it alienates itself from the Arab World due to the ongoing conflict in Iraq. At the same time, the Americans are supporting Israel, so nothing develops there. Therefore, they likely join the Third Bloc with India and Yugoslavia (whatever it was called) or develop their own bloc.