The latest Opinium/Observer poll published on Sunday (19 January) suggested 52% of the British public aged over 18 would vote to leave the EU tomorrow, a small increase since last November when 50% said they would vote to leave.
Sunday's poll, carried out by Comres for the Independent on Sunday newspaper, also suggests the anti-EU and anti-immigration policies of the UK Independence Party (UKIP) remain popular even though Cameron has already deployed tougher rhetoric on both issues.
Vince Cable, Britain's minister for business, is reportedly telling foreign investors there was a 5% chance his country would leave the 28-nation bloc.
Asked by the newspaper whether foreign companies had raised concerns, Cable said: "The answer is yes. What I say (to businesses) as a government minister is that the risks of us leaving the EU are very, very low … and I just try to reassure foreign investors."
UKIP is Britain’s favourite
The poll spelt more trouble for the Conservative British Prime Minister David Cameron.
Britons named UKIP as their favourite political party in the poll, dealing a setback to Cameron ahead of elections to the European Parliament.
The survey came days after another poll showed Cameron's Conservatives are set to finish behind UKIP in the May election, meaning they are on course to finish third in a nationwide vote for the first time.
Though UKIP has no seats in the British parliament, its popularity is a problem for Cameron because it threatens to split his own vote at a national election in 2015, depriving him of outright victory.
Its strong poll ratings also worry eurosceptic lawmakers in Cameron's own party who want him to adopt a tougher anti-EU stance, something he has balked at, raising the possibility of a damaging internal rift of the kind that contributed to the downfall of the last two Conservative prime ministers.
If the Conservatives do particularly badly at the May elections for the European Parliament, a significant number of eurosceptic lawmakers are threatening to stir up trouble for Cameron.
UKIP has 13 seats in the European parliament and took a quarter of the votes cast in local elections in May.
It wants Britain to leave the EU and an end to what it calls "open-door" immigration. There is evidence it has siphoned support from all political parties, but it has attracted a large number of former Conservative voters in particular.
The poll, which interviewed a sample of 2,029 Britons earlier this month, found 27% of them had a favourable view of UKIP, more than any other party.
By contrast, 25% said they shared the same view of Cameron's Conservatives, with 26% expressing the same opinion about the opposition Labour party.
Only 14% said they had a favourable view of the Liberal Democrat party, which is in a two-party coalition with Cameron's Conservatives.
Nigel Farage, UKIP's leader, also scored highly, with 22% of those polled saying they had a favourable view of him, a rating second only to Cameron's who scores consistently highly in polls about his leadership qualities.
The poll came as UKIP was battling to restore party discipline after one of its local councillors in England caused it embarrassment by saying recent flooding across Britain was God's punishment for parliament backing gay marriage.
Cameron has promised to try to renegotiate Britain's EU relationship if re-elected in 2015 and to then offer Britons an in/out membership referendum.
Labour, which polls show remains a narrow favourite to win in 2015, does not favour a referendum.