A similar poll published last week by ICM found 44 percent of voters wanted to remain in the EU compared with 46 percent who wanted to leave.
Conducted between April 29 and May 3, the survey was weighted to take into account the likelihood of respondents actually voting in the June 23 EU membership referendum based on their comments, ICM said.
PM David Cameron is campaigning for the UK to stay in Europe.
A separate poll for the Observer newspaper on Sunday showed the campaign to stay in the EU had a one percentage point lead over the those who wanted to leave.
Meanwhile, a report published Tuesday by the Adam Smith Institute warned that the EU would make it difficult for the UK to negotiate a tailored deal, in order to discourage other member states from trying to leave.
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