AHC: One or more former British ME mandates or territories become members of the Commonwealth

Your challenge is make it so one or more of the former territories and Mandates formerly occupied by the United Kingdom in the Middle East becomes a part of the British Commonwealth either in the same vein as India where they are not ruled by the Britain, but enjoy the benefits of Commonwealth membership or in the same vein as Australia, where the monarch of England is the symbolic monarch of (Insert country name here) and there's a Governor General.
 
I wonder if they'd have been more likely to join if King George VI had still been alive when they gained full independence rather than having a woman as Head of the Commonwealth? Then again it could be that the Head of the Commonwealth is also the Supreme Governor of the Church of England that put them off.
 
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