It was a bit earler than WWII Bob. The Balfour Declaration of 1917 is what set the scene.
http://en.wikipedia.org/wiki/Balfour_Declaration_of_1917 By 1948 the UK government had given up and just walked out and left the various sides to fight it out.
The early attacks in 1948 were not to establish a Palestinian state but for the neighbouring countries to carve the place up among themselves. Egypt controlled the Gaza strip with an iron fist up until 1967 and Transjordan (created out of East Palestine) took over the West Bank and dropped the 'Trans' from it's name when it annexed the territory. The Arabs of the region have been fought over but not part of the process until very recent times when Jordan dropped it's claim to the West Bank. Jordan still has a toe in the water through it's connection to Muslim holy sites in Jerusalem.