The British had explained thoroughly in writing to Arab leaders after 1919 that they had never promised them a state on the west side of the Jordan river.
The Arabs continued to press their case, and by 1947 had been able to coerse/convince the British and others that they should split Palestine once more and create yet a third Arab state. Which is what occured as witnessed by UN resolution 181.
You have to realize that the word "Palestine" has many different meanings depending on what time frame you are talking about (or who you are talking to). To this day the PLO prints maps depicting all of Jordan as "Palestine", and indeed, after WW1 Palestine meant the land that is now Jordan, and Israel, and the territory claimed by the "Palestinians".
The Feisal Weizman agreement of 1919 did not provide for a jewish state in Palestine. The agreement provided for "cordial understanding" between Arab and Jew and "to encourage and stimulate immigration of Jews into Palestine on a large scal and as quickly as possible to settle jewish immigrants upon the land through closer settlement and intensive cultivation of the soil." The agreement had a protective clause stating, "In taking such measures, the arab peasant and tennant farmers shall be protected in their rights and shall be assisted in forwarding their economic development."
The english text of the agreement included a reservation written in Feisal's own handwriting stating,
"Provided that the Arabs obtain their independence as demanded in my memorandum dated the fourth of January 1919 to the Foreign Office of the Government of Great Britain, I shall concur in the above articles. But if the slightest modification or departure were to be made, I shall not then be bound by a single word of the present Agreement which shall be deemed void and of no account or validity and I shall not be answerable in any way whatsoever."