Actually the creation of israel began much earlier that after WW2. England announced it's Support for a jewish state in 1917, with the Balfour Declaration (https://en.m.wikipedia.org/wiki/Balfour_Declaration). I think it was to gain the support of their jewish population in the war.

Later in they were not so eager to create a jewish state anymore, because tensions in the region were already high. But they lost their colonial mandate for palestine in 1948 and the US began to support the idea of a jewish state a little before this.