Well, it wasn't quite that simple. Don't forget, Britian did everything they could to ensure that the Jewish State would be "still-born" - exterminated by the Arabs whom they allowed to arm while restricting arms to the Jews. They hoped that they could persuade the UN to intervene so that Britian could go in and "save" whatever Jews were left after the Arabs massacred them. Of course, any dream of a Jewish State would have been dead after that and the Jews would have to be content to rely on others for their very existance. It appears that to this day the Brits are sorry it didn't work out that way.
But explain how the '56 Suez War fits in: weren't the Israelis with the Brits on that one, against the Egyptians?