Comment: Resolution 181

came AFTER Britain had already started to withdraw and they may in fact have already been completely out (both came in the same year - '47). The UN had nothing to do with the British withdrawal. This left the Arabs and Jews occupying the Palestinian province to fend for themselves. The Jews had every intention of setting up their own Jewish state (many of them and/or their parents had migrated to Palestine for that express purpose).
Res. 181 recommended "the adoption and implementation, with regard to the future government of Palestine, of the Plan of Partition with Economic Union." Jerusalem was to "be established as a corpus separatum under a special international regime and...be administered by the United Nations." http://domino.un.org/unispal.nsf/0/7f0af2bd897689b785256c330...

Israel accepted it, but, the Palestinian Arabs rejected it because they didn't want a "partition," they wanted the Jews to get out of Palestine.

If the United Nations had not existed, the history of Israel would not be much different than it has been. The Jews and Arabs would have competed to fill the administrative vacuum left by the Brits, resulting in war, resulting in Arab defeat, resulting in hundreds of thousands of Palestinian refugees, and resulting in the Jewish-run state of Israel. All Resolution 181 did was get the fighting started and over with sooner.