Flagging a problem: misconceptions in Britain about what the EU does - and how much it costs - remain rife. Photograph: European Communities 2009

A poll just carried out by the European Commission's London office of popular British attitudes towards the EU gives more grounds for optimism than recent elections to the European Parliament may suggest.

True, just over a third of voters (35 percent) turned out for this June's poll and nearly a quarter of them supported parties which want Britain out of the Union. Eurobarometer surveys have for years shown that a fair chunk of Brits dislike the EU (particularly the older, less formally qualified and more rural they are) even though most do not know what it does and do not seem to care much that they don't know. But we wondered how far people who have internalised many of the benefits of the single market would really be ready to forgo them, and conducted the poll to find out which bits of EU activity were on the public radar map and how important people found them.

The most surprising figure to emerge concerned the size of Britain's net contribution to the Communities' budget. The average given by respondents worked out at a jaw-dropping 23 percent of gross national income (although nearly half had no clue). The actual figure is around 0.2 percent.

Respondents were pretty evenly split on whether the benefits of membership outweighed the drawbacks. But they did see a role for the EU in issues of cross-border impact, with around four in every five supporting its involvement in protecting human rights, and in dealing with climate change, terrorism and the financial crisis. Questioned on whether certain initiatives had benefited Britain specifically, clear majorities gave the thumbs up to the single market (67 percent), environmental legislation (58 percent) and the greater clout accruing to the country in world trade negotiations. Even 49 percent said working conditions had improved (against 46 percent who did not).

On awareness of various EU initiatives, half knew about the European Health Insurance Card, but fewer than one in five were aware of the Bathing Water Report or the European Arrest Warrant, which enabled one of the bombers from the July 21 2005 attacks on London to be extradited from Italy. Even here, however, the sample group agreed by and large on the importance of these initiatives, whether they had previously known of them or not.

In the final set of questions, we asked our 1,000 respondents whether they would mind losing the benefits of EU membership if Britain pulled out and was unable to secure a free-trade deal. Significantly for the debate on whether withdrawal has a genuine and sustained political constituency in this country, five times as many said they would care as wouldn't.

Eurocrats often get berated for suggesting that people criticise the European Union because they do not know about it, when in fact they do and just do not like what they see. This would be easier to swallow had more than eight out of ten respondents in our survey (following the pattern of recent years) not claimed to know little or nothing. On top of this, about half felt there was a general media bias in reporting on EU affairs, with written press reports seen as the biggest culprits.

If the data in this poll are repeated, it suggests that Britons may be hazy and sniffy about the Union, but even if the organisation itself attracts little affection in the country, a good many of its outputs apparently do. It is not unreasonable to think that the public acceptance of it might grow – or at least hostility fall – if it were better known in Britain for its real primary remit as regulator and watchdog of the world's biggest market in the world and its externalities.