Two-thirds of British voters said that they wish to remain in the EU, while just 22 per cent would vote to leave, according to a new poll.
Excluding those who did not know, the result would come out at 75-25 in favour of staying in Europe, according to the poll, by Ipsos Mori.
The news comes as Cameron continues his diplomatic push to court EU leaders in a bid to renegotiate Britain's relationship with the EU, while at home, seven Eurosceptic MPs have begun to set up the "Out" campaign.
The poll, conducted for the Evening Standard, used the exact wording expected to be used in the 2017 referendum.
It found 63 per cent of Conservatives and 76 per cent of Labour backers would vote to stay in the EU - while almost all Ukip supporters would vote to leave.
Some 57 per cent of those polled said they were "not confident" in David Cameron's ability to get a "better deal" for the UK, while 38 per cent were confident.
Gideon Skinner, head of political research at Ipsos Mori, said:
Support for staying in the EU has been growing since well before the election and now stands at a 24-year high — even if some would prefer a less political union.
But at the time of the 2011 eurozone crisis the ‘outs’ were in the lead — so another crisis could see attitudes change again.