It didn't really. By war's end Great Britain had done a complete 180 on the Balfour Declaration, insisting it didn't propose Jewish sovereignty in Palestine. At best a Jewish minority, their rights respected, would reside amid an Arab majority. Seeing how well the British managed the multiple pre-war Arab riots when they were there in force, one can imagine how well they'd ensure Jewish rights were respected after they left.

No. WWII was in many ways a war for petroleum, and Britain, along with France & the other powers sought to appease the oil-producing Gulf states. And who can blame them? Nations don't allow sentiment to preclude their strategic interests. When Labor came into power foreign minister Anthony Bevin proposed Jews simply "go home" back to those European nations where their erstwhile neighbors murdered survivors or drove them away so as to avoid returning the homes & land they had taken in their absence.

And, incidentally, on the subject of former mandates (which Egypt is not, not really), you left out Jordan (formerly Transjordan), a monarchy that has enjoyed good relations with Israel, even before their formal treaty.