What if: Iraq-Iran War of 1939

  Well that force would be a serious problem for the British and Iraqis, assuming that at least some of the latter wouldn't want to side with the Iranians, which some might, at least in the short term.  You would probably see much of the BEF actually ending up in the ME fighting this threat, along with forces from the southern dominions and India.  The other factor is how much Britain and others have responded to the TTL Iranian converison to some form of fascism and build-up as there will have been some reaction.

  Another issue is what would Stalin think of it.  Even with the OTL pact with Hitler he's not going to be happy with a pro-German Iran both building up a larger military and then going on a conquering spree.  Especially since I can't see such a conflict being restricted to Iraq.  Even if the Iranians took it all and didn't want to go any further, which seems unlikely Britain would seek to restore control of Iraq as it was too important to them, along with other resources in the area.  Plus if Iran is doing that it would definitely seizing the British interests in Iran, including the oilfields in the SW.

  Depending on the size and quality of the Iranian forces at least some of the regular forces of the BEF could well be necessary.  Australia had only a few divisions at the start of the war and S Africa had less and initially restricted them to deployment in Africa south of the equator.  India has substantial forces at the start of the war but as well as being needed in India, Malaya and Egypt/Palestine I'm not sure how many had been fully mechanised at this stage which would be a big issue.  The BEF wasn't that large itself, with conscription only coming in ~6 months before the war started so it may be seen as more practical to send it as a unit to ensure defending Iraq and defeating Iran quickly before any fighting in NW Europe.  Especially since it would seem to be unlikely that a major offensive would occur during the autumn and winter with the bad weather.  [Hitler did want an offensive in this period but between the weather and the need to replace losses after Poland his generals managed to talk him out of it]. 

  The ideal option for the allies would be to defeat Iran quickly, try and replace the government with a friendly one, although that could mean keeping a garrison there and is likely to lead to tension with the Soviets.  Then have the regular forces moved back to Europe in time for spring and any German attack.  Which would probably go pretty much as OTL and possibly then prompt further problems in Iran.

  Well Britain still has Kuwait and what's now the UAE regions as well as friendly relations with Oman.  Furthermore at this point even if pretty much all of Iraq is lost France is still an active ally so allied forces could operate from Syria.  However an amphibious attack at some stage could be likely if Iran has significant initial successes.

  In terms of the eastern border Iran has a land border with British India - what's now southern Pakistan.  The terrain isn't that great for offensive action but the Baloch people of the region have elements in Iran, Pakistan and Afghanistan and might be friendly to an allied move given that a fascist Iran is likely to be unpopular with its non-Iranian minorities.  This could also apply to the Kurds, Azerbaijanis and possibly the Arabs of the SW as well.  So some sort of overland operation from the east and support of minorities in the west could well be useful for the British.  Although supporting Kurds will be an irritant for Turkey and Azerbaijanis for the Soviets.

  The best bet for the allies might be a relatively short and bloodless conflict that sees the Iranian fascists defeated and a 'friendly' government which includes a fair amount of power to the regions and minorities, although this is likely to be deeply unpopular with the Iranian core territories so could lead to problems further down the line.

  If they get past Basra then almost certainly.  Not sure if its oil is known of at the time but simply an Iran that's attacking a British protectorate is at war with Britain so its got to remove all British bases which can threat them, which is a very tall order.

  A better alternative for Iran might be a more cautious pro-Nazi dictatorship that sits tight until after the fall of France.  With that blow and also Italy in the war then Iran has a markedly greater chance of making gains and then possibly even forcing some sort of favourable peace with a vastly overstretched Britain.  Of course when Barbarossa starts their almost certainly toast because they will have the Soviets attacking from their north as well as the British from other directions.