Fixing the Middle-East...sorta

In my AAR ( linked in my sig ) I am coming close to a point where I want to try and have the British attempt to 'fix' the middle east. The main problem IMHO is what to do with Palestine. My idea was a two-state solution ( exact borders to be determined ) and an international or British administration of Jerusalem with everyone guaranteed equal access to the Holy sites by London. I don't know if this would work. Suggestions anyone? Bear in mind this is 1940.
 
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