Nearly half would vote to leave while only 37% would vote to stay, though the picture changes if membership is renegotiated

British people would vote to leave the European Union by a large margin under the current terms of membership, according to a new Opinium/Observer poll.

But David Cameron could turn public opinion round and keep the UK in the EU if he is able to negotiate new and improved terms of membership, the survey suggests.

Opinium found a total of 48% would definitely or probably vote to leave under present rules, while 37% said they would definitely or probably vote to stay in.

However the poll suggests the tide could be turned if David Cameron, who has promised to hold an in/out referendum by the end of 2017 if the Conservatives win the next election, does manage to secure a favourable renegotiation of terms.

In that event, 42% say they would either definitely or probably vote to stay in, against 36% who would probably or definitely vote to leave. There is widespread scepticism, however, over Cameron's ability to achieve a satisfactory renegotiation. Only 18% (including 34% of Conservatives) think he will win the necessary concessions.

The findings underline the risk that Cameron faces. If he puts a vote to the British people having gained only minimal concessions , voters may oppose his party's policy of remaining in the EU and vote to leave. In this scenario his authority would be damaged to the point where many would question his ability to remain prime minister.

With Cameron facing an EU summit this week, at which his attempts to block federalist Jean-Claude Juncker from becoming the next president of the European Commision are likely to fail, voters were also asked if the appoinment of the former Luxembourg prime minister to the top Brussels job would affect their decision in the planned 2017 referendum.

Some 27% said it would have some sort of effect, while 43% said it would not and 28% did not know.

After a difficult week for Labour leader Ed Miliband, there is some relief as Labour's poll lead holds steady over the Tories at four percentage points. Labour is unchanged on 35%, the Conservatives are also unchanged on 31%, Ukip is down two points to 17% and the Lib Dems are up one point on 7%.

Intention of voters in 2015 UK general election. Photograph: Guardian

But Miliband's personal ratings remain poor with only 23% approving of the way he is leading Labour and 49% disapproving. David Cameron fares better with 37% approving and 47% disapproving.