Under the terms of the Mandate, Britain's principal obligation was to facilitate the implementation of the Balfour Declaration of November 2, 1917, which pledged "the establishment of a national home for the Jewish people."(2) No territorial restrictions whatsoever - neither east nor west of the Jordan River were placed on the Jewish National Home. In fact, the Mandate stipulated that Britain was to "facilitate Jewish immigration under suitable conditions and shall encourage close settlement by Jews on the land."(3)
You'll note a rather large Jewish homeland by modern standards,
Then, the British partition in 1946:
). In was only in 1946, 24 years later, that Britain unilaterally granted Transjordan its independence. (2) With Transjordan's independence, the British had partitioned Palestine and created an independent Palestine-Arab state.
And finally 1947 UN partition
On November 29, 1947, the General Assembly of the United Nations voted with a 2/3 majority to partition western Palestine into a Jewish and an Arab state.(1) The Jews were to be granted what appears on the map in blue. Over 75% of the land allocated to the Jews was desert. Desperate to find a haven for the remnants of European Jewry after the Holocaust, the Jewish population accepted the plan which accorded them a diminished state. The Arabs, intent on preventing any Jewish entity in Palestine, rejected it.
And the 1949 armistice
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You'll note an Arab state on the West Bank did exist on paper at least for about 2 years before Jordan, not Israel, anexed it.