REUTERS/Yves Herman
Britain's Prime Minister David Cameron and U.S. President Barack Obama hold a joint news conference at the end of a G7 leaders meeting at European Council headquarters in Brussels June 5, 2014.
The online survey taken on Monday and Tuesday showed support for the Out campaign had risen 3 percentage points to 42 percent since a similar survey on April 12-14, while support for the "In" campaign had risen 1 percentage point to 41 percent.
The proportion of those who said they did not know how they would vote fell 3 percentage points to 13 percent, according to the YouGov poll.
U.S. President Barack Obama on Friday warned Britain would be "in the back of the queue" for a trade deal with the United States if it left the EU, an unusually strong intervention which "In" campaigners welcomed.
Brexit advocates were not as welcoming, though. Prolific Tory backbencher Jacob Rees-Mogg wrote in a Mirror opinion piece that the US President's intervention was "arrogant" and "unwelcome," and said it would inadvertantly give a boost to the Leave campaign as the British public would view the President as condescending.
Betting odds moved sharply in favour of Britain voting to remain in the 28-nation bloc after the President's London visit. Bookmakers Betfair and Ladbrokes both indicated that the vast majority of referendum bets were being placed on the Remain campaign being victorious on June 23. Yet, the results of the YouGov survey suggest Obama's remarks haven't yet had this impact on public opinion.
The YouGov poll also suggested a big boost for the UK Independence Party (UKIP), which has campaigned to leave the EU.
The poll showed UKIP leader Nigel Farage was now more trusted on Europe than Prime Minister David Cameron, with 23 percent saying they trusted Farage and just 20 percent saying they trusted Cameron.
Though the Out campaign was in the lead, 35 percent of voters said they trusted Obama on Europe while 32 percent said they trusted Boris Johnson, the leading member of the "Out" campaign.