Tory members trust David Cameron on the EU. Here's the poll that proves it But they probably recognise this already. A comprehensive survey of ordinary Conservative Party members carried out, with the help of YouGov, by me at Queen Mary, University of London and my collaborator, Paul Webb, at the University of Sussex, suggests that the overwhelming majority of grassroots Tories think Cameron is doing a good job. True, 23 per cent, many of them at or nearing pensionable age, think he's doing badly. But they're clearly outnumbered by the 76 per cent who think he's doing well - a proportion that climbs to around 85 per cent if we look at the under-forties. Even more interestingly, our survey suggests Cameron retains enough appeal among his own his own party members to persuade them to support whatever renegotiated package he manages to come back with, in advance of an in-out referendum. Asked how they would vote were a referendum on Britain's membership held today, some 71 per cent of ordinary party members would vote to leave, the only significant difference being between those living in London (who seem to be rather less Eurosceptic) and the rest of the country. Only 20 per cent of the total said they would vote to stay in. Asked, however, what they would do if Mr Cameron, having achieved a deal which he claimed protected Britain's interests, recommended the UK remain in the EU, large numbers of ordinary Tory Party members changed their tune. In that case, the better-off-out vote nearly halved, to 38 per cent, while the best-stay-in vote almost trebled to a winning 54 per cent. Of course, one can try to dismiss the idea that Prime Minister's retains the power to persuade by pointing out that these are, after all, his own party members. One would expect them to moderate their views given the right cues from the top - just as they did when Edward Heath was their leader back in the Sixties and Seventies. On the other hand, the Conservative grassroots are probably some of the most convinced Eurosceptics around right now. If even they can be persuaded, then surely the rest of us probably can be persuaded too? Whether all this will give the most determined sceptics among Mr Cameron's MPs at Westminster pause for thought, or whether it will instead make them all the more keen to get rid of him at the earliest possible opportunity, no doubt only time will tell. The survey was of 852 members of the Conservative Party throughout the UK, with fieldwork conducted between May 31 and June 11 2013. Tim Bale is Professor of Politics at Queen Mary, University of London