While it's true that the Zionist movement had existed since the end of the 19th century and had gained some measure of political support, there's no denying that the Holocaust provided the US and Britain with a sense of immediacy that the Jewish people were in desperate need of a homeland where they could attempt to recover their population and culture after all the trauma that they'd just suffered. Even back in the 1880's, Palestine was the obvious choice for religous Zionists who couldn't imagine a Jewish homeland anywhere but Palestine/Israel-Judea/Canaan. These Zionists received some sizable support, even then, from American Protestants. The bulk of the movement however were secularlists who felt that a homeland was needed in light of growing anti-semitism in Europe and Russia. They weren't as married to the idea that the new nation had to be Palestine, although they appreciated the historical significance of the area to their people. Among the other places considered were Argentina and Uganda. Uganda was even considered as a possible temporary safe haven for Jews eager to leave an increasingly hostile Russia until a permanent homeland could be chosen.
As annoying, offensive, and generally childish as most CTs are, Holocaust denial is just a whole league of it's own. Only a demented mind can ignore so much evidence, so coldly, and then turn around and callously blame the victims as the masterminds.