The survey showed that 39 percent of voters backed Britain staying in the 28-member bloc level pegging with the support for withdrawal. Five percent said they would not vote while 17 percent were undecided, the online poll of 1,693 people carried out on April 11-12 found.
The previous YouGov survey, carried out a week ago, had the remain camp on 40 percent and the leave campaign on 38 percent.
The latest survey comes after a difficult week for Cameron who has faced criticism and scrutiny of his personal wealth after he said he had profited from selling shares in an offshore fund set up by his father which had been revealed in the Panama Papers.
That led him to taking the unusual step of publishing a summary of his tax records for the past six years.
The YouGov poll found public trust in Cameron, who is the effective head of the EU “In” campaign, had fallen 8 percentage points to 21 percent since a comparable survey taken on Feb. 21-22 poll.
It showed trust in opposition Labour leader Jeremy Corbyn had risen 2 percentage points to 28 percent. Corbyn is due to make his first major intervention in the argument over Britain’s EU future later on Thursday when he will put his weight behind the “In” campaign.
However, trust in London Mayor Boris Johnson, the flamboyant, popular leading face of the “Out” campaign, has also fallen 8 percentage points to 26 percent, the survey indicated.
The “Vote Leave” group, which is backed by Johnson, was on Wednesday chosen to be the official “Out” campaign ahead of a referendum on June 23.