Why did Britain give her support to the Palestinians and Arabs in the years leading to 1948 ?

Britain nurtured and trained Zionists gangs. If you are talking about the white papers, it was a temporary appeasement that did nothing, because they were busy with WW2, and didn’t want to fight the Arabs as well at the same time. Britain always favored and sided with the Zionist movement, its child colonial prodigy.
Lord Balfour (who gave the Balfour declaration to Zionists) , and Winston Churchill were well known Zionists.