Because Britain was almost as anti-Jewish as Nazi Germany.
Yes, they do seem to wear out their welcome wherever they go.
That said, it was the British who came up with the Balfour Declaration to try to settle the place with Proxy Colonists to expand their influence. The funny thing is, between 1919 and 1945, not a whole lot of Europe's Jews were that keen on the idea.
That changed after the war... But the concept of giving them the Palestinians' land because Europe felt bad about the Holocaust is like me giving away your house to a black family because I feel bad about slavery.