Quoted:
Also, how did the British come to be in control of this important piece of land?
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The British came to control Palestine after WWI. Before that, it was a province of the Ottoman Empire. The British controlled Egypt since....gee, I don't know when they took control of Egypt. Probably after they defeated Napoleon.
But in WWI, the Brits organized the Arabs in a revolt against the Turks who were aligned with Germany and Austro-Hungary. After Armistice, the Brits and France split up the Mideast with the Balfour Plan of 1917, creating Palestine (You can see all this in Lawrence of Arabia).
Since the Arabs helped them defeat Turkey, the British clearly favored the Arabs in their administration of Palestine, especially once oil began to be discovered and developed in Arabia.
A small number of Zionist Jews had been coming to Israel from Europe for decades, setting up communal farms and settlements as part of the ultimate goal of seizing Israel for themselves and re-establishing a homeland. This migration really stepped up after WWI. The Brits weren't too keen on this and suppressed them. The Jews fought back with a guerilla war (which you can see in the movie, Exodus)