Who controlled Palestine before world war 2?

Answer 1

"Before WW2" is a lot of historical landscape. Here's a simple breakdown:
As the answerer below identified, Britain was the last foreign power in control of the region known collectively as Palestine. Before them it was held by the Ottoman Turks, given to them after the British took it back from Muhammad Ali Pasha of Egypt and the Sudan. Muhammad Ali took it from Abdullah Pasha of Acre who was given the region by the Ottomans. Saladin held it at the end of the Crusades, after he took it from the Fatmids in 1187, who took it from the Seljuk Empire in 1098. The Fatmids held it for a time before the Seljuk Empire, after they took it from the Abbasid Caliphate in 878, who had taken it from the Umayyad Caliphate in 750. The Rashidun Caliphate, the legacy of none other than the son in law and nephew of the Prophet controlled the region until it passed to the Umayyad. The Byzantines owned the region until 628, having taken it from the Sassanids, who taken it from the Palmyrene Empire, who had been given the region by Constantine. The Eastern Roman Empire had acquired the region with the fall of the west under Rome, who held the area and had broken it up into five regions. Before the Romans, the area known as Palestine had been kicked around and passed back and forth by nearly every ancient kingdom and empire in the area from before it was conquered by Alexander the great. Before Alexander, it was held by Egypt, Assyria, Persia, Babylonia, Judah, and Israel. Biblically speaking, before Israel moved in, it was a loose arrangement of local cities that were held by a variety of tribal groups.

Answer 2

Jerusalem was under control of the UN as an city of International importance. Great Britain had previously held the city under mandate of the League of Nations following WWI.

Answer 3

Britain