Well, the Labour Party will not save you. (In a weasel defense, let me state that the prediction at the link was that Labour will win if Scotland walks. But see below: we did think that Labour would win anyway, and we was wrong.)
Still, I am not worried. First, the polls augur well. The blue dots show support for the E.U. The green dots show support when asked, “Imagine the British government under David Cameron renegotiated our relationship with Europe and said that Britain’s interests were now protected, and David Cameron recommended that Britain remain a member of the European Union on the new terms. How would you then vote in a referendum on the issue?”
As long as David Cameron can finagle something out of his European partners, these numbers make it seem like it would be an easy sell to the British public. As long as “something” does not involve a treaty change, I suspect that the rest of Europe would be quite willing to go along. Unless he humiliates himself, he should be able to get a pro-E.U. majority without breaking a sweat.
Now, should we trust the polls? After all, they got the recent general election fairly wrong. But I would make three points. First, constituency polling is much harder than national polling. That said, there is evidence that the polls actually blew the national vote share, so that might not be as much consolation as you would hope.
Second, the reason the national vote shares were off appears to have the last-minute collapse in Liberal Democratic support. That is tactical voter behavior consistent with the model that Victor Menaldo explained in comments: try to create momentum for your party by telling pollsters how you want to vote, but then bail out for whichever leading alternative you dislike less when election day rolls around. In a two-option referendum, tactical voting is not an issue. The polls should be more accurate as a result.
Finally, the general election trend was against the Liberal Democrats and in favor of the Conservatives. (Click on the vote forecasts tab.) If the numbers turn around in the next few years, then we will revise our forecast, of course.
But what could destroy the pro-E.U. momentum? It is hard to see anything. UKIP would have to make some pretty damned convincing arguments to sway these margins. Or Cameron would have to royally botch things up in Brussels and Berlin. Even a recession would not do it; people are less likely to take risks in bad times.
In short, much ado about nothing.
Unless the above is wrong. What could make Brexit a contender?