dj, There were various 'Israel's in biblical times, not always called Israel and only roughly corresponding to the current state of Israel.
I'd put a link, but the Link Police might jump on me and I'm a scaredy cat. Anyway, you're a big girl and know how to use Google. ;-)
The whole area was conquered in the 7th century and the population was predominantly Muslim with other substantial minorities until the 20th century, when the Ottoman Empire was on the losing side in WW1.
Various groups (Zionists in the original meaning of the word) wanted a Jewish homeland centred on Jerusalem throughout the nineteenth and twentieth century. They didn't stand much chance when the Ottomans were in control, but put increasing pressure on various governments (including the British) after WW1. Ironically, they were considered to be terrorists. The Jewish Agency bought up land in the area and the British, who had a mandate in Palestine, wrote the Balfour Declaration, but dragged their feet about establishing a homeland.
WW2 forced the issue, which is why some people think that Israel was born out of guilt - they have a point. The British have nothing to be proud about, because they refused to open up Palestine during the pre-war years as a safe haven for persecuted European Jews. The Nazis wanted to rid Germany of Jews and were very happy to pack them off to Palestine. It was win win for them, because the Jews were forced to leave their money and possessions in Germany.
Invading Poland presented the Nazis with a bigger problem. Polish Jews were generally poor and couldn't afford to emigrate, so the Nazis tried to starve and intimidate them. Some locals helped with murdering some of them, but this wasn't quick or effective enough for the Nazis, so the idea of the death camps was born.
Historians are correct that there was no state of Israel until 1948. However, many people just accepted that the area was called Israel, because that's what the Jews themselves called it. Ironically, today many countries don't recognise Palestine as a sovereign country and the situation isn't that different. I suspect that's the point LIvingstone was trying to get across, but he managed to be offensive and his facts were muddled.