Menachem Begin’s family (parents, brothers, etc.) were waiting to immigrate to British Palestine, but the route was closed by the White Paper. Instead, they were massacred by the nazis (all on one day).
British policy then was to appease the Arabs.
British policy today doesn’t want Jews in Jerusalem or the West Bank (again, to appease the Arabs).
Nothing has changed in that regard; but there is no reason for Jews to pay heed.
The British took on Palestine and as a Brit, I prefer to see us as a middleman stuck between two groups, each claiming exclusivity for the land. Perhaps the British didn’t get it all right, but would America or France or anyone have done any better?. I see us as piggy in the middle, pleasing nobody and hated by both sides.
British policy today is like everyone else, its to try and get a peace to that (what should be a) lovely part of the world. Peace between people. NOT actively against Israel.