Ipsos MORI’s telephone poll shows Leave on 53 percent and Remain on 47 percent among likely voters, excluding undecided voters.
John Curtis of the British Polling Council said despite referendum polls often overstating an “appetite to change”, once Leave are at 52 per cent or 53 per cent it signals a significant turning point for Brexit.
Ipsos MORI’s previous poll in the middle of May had an eighteen point lead for Remain among all voters, which means today’s results reveal a distinct sea-change in the campaign,
A poll by Survation has also shown a swing to Leave with 45 percent intending on voting out and 42 percent wanting to remain, with 13 percent undecided.
In an interview with the BBC’s Daily Politics show, Mr Curtis said: “If you take the phone polls this week they marginally put Leave ahead. The internet polls have also been putting Leave ahead.
“They seem to be converging around a picture where Leave probably now have a narrow position of around 52 to 53 percent of the vote.
“Which I think takes us to a crucial point. One thing we are aware of abour referendums is that they often overstate the appetite for change.
“We might think that some voters will go back towards remain as they are concerned about the risks in the last week. But once Leave are at 52 or 53 in the polls, we have reached the point where the Leave side have a 50 percent chance of winning.”
Since the beginning of June all of the polls released have shown the horserace somewhere between a tight race and a clear Leave lead.
After the past three weeks of intense campaigning however, Leave are now pulling ahead.
Since May 27 when the official short campaigning period got underway, the UK Government lost the support of the civil service, which had previously given them considerable abilities to dominate the campaign.
One of the last polls to show a clear Remain lead were ORB and Survation back at the end of May.
However the bookies still have better odds for Remain with Ladbrokes showing Remain at 62 percent - up two percent - and Leave down two percent at 38 percent.
Matthew Shaddick, Head of Political Betting at Ladbrokes said odds on George Osborne still being Chancellor by the end of the year had also shortened after he pledged to run an emergency budget if Britain leaves the EU.
He said: “Remain may have pulled back following some big bets in recent days, but after George Osborne’s battle with other Tories yesterday, the odds of him going by the end of 2016 have been shortened to 5/2.”