That's not entirely accurate at all. There was indeed a UN decision to partition the land and to acknowledge Israel, but no one was enforcing it. The Arabs and Jews were left to battle it out in a horrible war. Jews were facing the real possibility of a second extermination only 3 years after the holocaust (I don't think I'm exaggerating the consequences of what defeat would have looked like had the Jews lost that war).
The British policy towards Jews in Palestine was not consistent at all, and at a certain point they sided with the Arabs and banned Jewish immigration to Palestine - even at the height of the holocaust.