You know this is nonsense - this is my understanding of why ...
Jews suffered terribly at the hands of the Nazi's and they asked the British if it would be ok to have a homeland in Palestine.
The demand for a homeland grew from the mid/late 19th Century to early 20th century, and the Balfour declaration came in 1917. The Balfour declaration was in any case quite non-committal.
"His Majesty's Government view with favour the establishment in Palestine of a national home for the Jewish people, and will use their best endeavours to facilitate the achievement of this object, it being clearly understood that nothing shall be done which may prejudice the civil and religious rights of existing non-Jewish communities in Palestine, or the rights and political status enjoyed by Jews in any other country."
Plus, many of the Jewish population came from (a) Russia and other Eastern European states and (b) other Arab countries - nothing to do with the Nazis.
They wanted somewhere where they could be safe and never persecuted again. The British said "sure, no problem, you can have Palestine" so the Jews moved in.
Jewish immigration grew from the early 19th century, although peaked in the 1930 and 1940s.
Britain definitely didn't say "no problem". Indeed, Britain opposed the foundation of a Jewish state in 1948.
The Palestinians said "WTF?" and the Jews said "Sorry, it's ours now. Out."
In reality, much of the land was sold by Arabs (admittedly absentee landlords) to Jewish immigrants. It's true that there has been Arab opposition to Jewish immigration right from the start.
Happy to be corrected as my understanding is nowhere near complete.