Only to an extent, ask anyone who's actually worked setting odds for a major bookies (not an area I'm massively familiar with but I've given odds makers the inf

Only to an extent, ask anyone who's actually worked setting odds for a major bookies (not an area I'm massively familiar with but I've given odds makers the info they used to create prices for markets a few times) and they'll tell you that the company doesn't require them to be bang on every time. Once a market is getting enough action, all they need to do is algorithmically adjust the odds to fit around the bets, and let the house edge do the rest. So essentially if everyone is betting big money on Britain leaving, they will adjust the odds such that that becomes the favourite. Having accurate pricing means that there'll be less margin of error to compensate for in odds changing, and means they (the bookies) are safer against big losses that could have been avoided, so for sure they do their best, but in this case I'd be shocked if doing their best wasn't just taking a combination of what the polls say and what their own betting stats show and merging them together (and while merging in their betting stats will help them set odds that make sense for them, it doesn't help improve the polls' chances of being accurate).