Almost as third as many voters want the UK to leave the EU as stay in - but around 12 million remain to be persuaded either way, a poll found.
The OnePoll survey of 2,000 adults for ITV suggested the "no" camp would outscore "yes" by 42% to 31% if there was an immediate referendum.
It also found high demand for a cap (60%) or even an outright ban (23%) on citizens of other EU countries being free to emigrate to Britain - with the public seeing EU immigration as a bad thing by 44% to 30%.
David Cameron fell short of such a move when he set out his demands for reform of freedom of movement rules.
The PM is instead seeking tougher welfare restrictions and deportation rights as part of a renegotiated package he would put to a referendum in 2017.
Mr Cameron backs EU membership but has signalled he could back the "no" camp if he fails to secure key reforms.
More than a quarter of voters are still open to persuasion either way, the poll found.
A 55% majority believed the UK "could do well outside" the EU and warnings that it would hit jobs and investment are not believed by a margin of 40% to 34%.
Despite the fears about new arrivals to the UK, 61% said British workers should be free to live and work anywhere in the EU.
The research was carried out for an ITV programme - Europe - The People's Poll: Tonight - which will be aired aired today at 8pm.
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