The Palestine part of the mandate was the Palestinian national homeland. The part of Mandate Palestine what was called "Transjordan" was (and is) the Hashemite Kingdom, not the Palestinian national homeland.

I think Winston Churchill trumps Sir Alec Kirkbride. Churchill said that the Jews may find a home in Palestine, but that the indigenous non-Jewish Arabs of that area also retained a right to live there, and that the Jews were forbidden from creating a Jewish state or attempting to rule over the non-Jewish Palestinians in the area they were allowed to regard as their home.