The land was not "England's", or more accurately 'Great Britain's", to cede.
That is correct. Britain never annexed or otherwise laid claim on that land. It was not theirs to give away and they did not.
Great Britain won the land from the Ottoman Empire in World War 1. To the victor go the spoils. And Britain promised the land to both the Jews and the Arabs. The Arabs inherited vast amounts of land and oil from the defunct Ottoman Empire. Considering the special relationship between the Jewish People and the Land of Israel, from where they gave the Bible to half-the-world, the British did not think that the Arabs would begrudge sharing one tiny strip of land out of their vast empire. Boy, were the British wrong about that one!