How did Palastine give up Jeruselem to the Jews?

I saw part of a doentary on the God channel about how Israel was created by the British. It was a very one sided, pro Jewish doentary. It claimed that a plane dropped leaflets over Palestine telling the Palestinian they have to leave the land. The order came from a british lord or something whose name translates to prophet. Apparently the Palestinians just got up and left Palestine after this with out a shot being fired. I find this hard to believe what really happened?