I doubt that the UK will leave the EU. Those poll numbers fluctuate wildly; a few months ago, a clear majority wanted to stay. There isn't a strong enough case to leave the EU: the "Out" camp will depend on arguments such as "Europe sucks" and "Look how bad things are over there", since this is ultimately where the fluctuations in poll numbers originate. There are maybe 30% of the population who will vote Out irrespective of any arguments made. On the other side, there are maybe 40% who will vote In similarly. So there are 30% of "swing" voters who might be persuaded one way or the other. The polls show that these swing voters are highly correlated with how much bad press the EU is getting right now. The recent surge in anti-EU sentiment, driven by the refugee crisis, has caused these swing voters to lean "Out". Therefore, expect a fair bit bad press about the EU in the coming months from Eurosceptic papers, and for the Out crowd to bang on about how much the EU sucks. Meanwhile, the "In" side will be able to make a positive case for staying in the EU, with all 3 major parties in support. They can also depend on better news about the EU in the future -- if the Eurozone economy picks up, if the UK economy starts taking hits while the EU isn't doing so bad, or as the refugee crisis disappears from headlines, the pendulum will swing back the other way. So this referendum will probably be won by the In campaign, (a) because they have a bit of a head-start in the polls, and (b) because their appeal to swing voters won't be so dependent on the EU looking crap compared to the UK.