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The survey by YouGov in the Times newspaper, taken in the two days after Cameron set out his proposed changes for Britain's relationship with the EU, represents the biggest lead for the 'out' campaign since the referendum wording was agreed last September.
The poll showed 45 percent of Britons would vote to leave the bloc compared with the 36 percent who want to remain, a nine-point gap that was up from the four-point lead the 'leave' campaign held last week.
Nineteen percent said they did not know or would not vote.