The WhatUKThinks average now puts "Leave" at 51 per cent against "Remain" at 49 per cent ahead of the June 23 vote that could see financial markets plunge and hit global economic growth if Britain votes to go.
The balance tipped in favour of "Leave" after two polls at the weekend and one today put them ahead.
The last time it put "Leave" in the lead was on May 12.
The "Remain" camp led by Cameron has warned of the economic dangers of leaving, while "Leave" supporters like former London mayor Boris Johnson have said they want to curb immigrants from other parts of Europe.
Cameron took part in an event with political opponents Labour, the Liberal Democrats and Greens to accuse "Leave" supporters of "perpetuating an economic con-trick on the British people".
"While they peddle fantasy politics, in the real world our economy is slowing because of the huge uncertainty hanging over Britain's economic future," Cameron said at the "Britain Stronger In" event.
"The risks of 'Remain' are massive," he said.
Conservative former prime minister John Major yesterday had accused Johnson, a charismatic politician with popular appeal, of being a "python" who could not be trusted, in a scathing personal attack.
Financial markets have proved volatile ahead of the vote and have been particularly so as the campaign has heated up.
The pound fell to 79.05 pence against the euro in Asian trading-its lowest level in three and a half weeks-and stood at around 78.61 pence against the euro at around 0910 GMT.
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