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The campaign to quit the European Union has surged into a six-point lead with exactly a week to go, a sensational Ipsos MORI poll reveals today.

In a dramatic turnaround since May, some 53 per cent now want to leave and 47 per cent want to stay, excluding don’t knows.

It is the first time since David Cameron pledged the referendum in January 2013 that Vote Leave have come out ahead in the respected monthly Ipsos MORI telephone survey, which is exclusive to the Evening Standard.

Immigration has overtaken the economy as the most important issue to how the public will vote, which is a significant boost to Boris Johnson and the Leave campaign.

The survey reveals massive distrust of claims made by politicians on both sides, but especially the predictions of doom after a Brexit made by Mr Cameron and Chancellor George Osborne, dubbed Project Fear by critics.

Among key findings are:

Only 17 per cent of people believe the Chancellor’s flagship claim that UK households will lose £4,300 and be permanently poorer after a Brexit, despite the analysis carrying the full weight of the Treasury. Some 70 per cent think it is a falsehood.

Almost half believe Boris Johnson is telling the truth when he says that Britain sends £350 million a week to the EU, even though it has been criticised as misleading by independent experts. The claim is believed by 47 per cent and disbelieved by 39 per cent.

More people think they will be better off in five years outside the EU than inside, despite Government warnings of lost jobs and lower incomes if Britain leaves.

Immigration is now the most critical issue, cited as very important to their vote by 33 per cent, up five points in a month, including just over half of leave supporters.

The economy has fallen to second place in the league table of important issues, down five points to 28 per cent.

A fifth of people say they might change their mind - which means the outcome is impossible to predict.

Overall the poll suggests a significant shift to the Leave camp in the past month, which coincides with the official Vote Leave campaign focusing more strongly on immigration.

Over half - 52 per cent - of people backing Leave list immigration as very important to their vote, while 41 per cent of remain backers cite the economy as very important.

Strikingly, in the battle of claim and counter-claim it is Mr Cameron who is coming off worst.

Ipsos MORI tested public attitudes to some of the most bitterly contested claims made by both sides, and discovered markedly greater scepticism about what Remain were saying.

For example, Mr Cameron listed six “complete untruths” by Vote Leave last week, including a claim that the UK is liable for future eurozone bailouts.

However, the poll found 48 per cent think the claim is true, and just 40 per cent think it is false.

EU referendum campaign - in pictures 34 show all EU referendum campaign - in pictures 1/34 Boris Johnson (left) kisses a wild salmon as he is shown around Billingsgate Fish Market in London with porter Greg Essex, uncle of TV presenter Joey Essex, on the final day of campaigning Stefan Rousseau/PA 2/34 A van displaying an advert saying 'Don't Wake Up With Nigel Next Friday' is driven through Westminster Jack Taylor/Getty Images 3/34 Michael Gove speaks alongside Priti Patel (left) and Kate Hoey at a Vote Leave campaign event at Old Billingsgate market, London Dominic Lipinski/PA 4/34 A passenger on a train reads the Evening Standard on the London Underground EPA 5/34 Delia Smith during the Channel 4 EU referendum debate Dominic Lipinski/PA 6/34 David Cameron appears on a special referendum edition of BBC One's Question Time, hosted by David Dimbleby Stefan Rousseau/PA 7/34 Jayne-Anne Gadhia, CEO of Virgin Money, speaks to Sir Richard Branson about his views on the EU referendum Ben Pruchnie/PA 8/34 JD Wetherspoon beer mats that have been printed by the pub chain with strong messages in favour of leaving the EU JD Wetherspoon/PA 9/34 Ukip leader Nigel Farage and Kate Hoey on board a boat taking part in a Fishing for Leave pro-Brexit "flotilla" on the River Thames Stefan Rousseau/PA 10/34 Liberal Democrats leader Tim Farron greets supporters after arriving in the Liberal Democrat Vote Remain campaign bus in east London Ben Stansall/AFP/Getty Images 11/34 Boris Johnson MP visits Sam Cole Foods fish processing factory in Lowestoft, Suffolk, where he was campaigning on behalf of the Vote Leave EU campaign Stefan Rousseau/PA 12/34 A boat carrying supporters for the Remain in the EU campaign, including Sir Bob Geldoff, shout and wave at Brexit fishing boats as they sail up the Thames Ben Stansall/AFP/Getty Images 13/34 Yvette Cooper MP gives a helping hand to her husband and former shadow chancellor Ed Balls, as he gets up from a story time session, during a Vote Remain canvassing visit to Shadsworth Children's Centre in Blackburn. Christopher Furlong/Getty Images 14/34 The Sun backs Brexit Daniel Sotrabji/AFP Getty Images 15/34 Eddie Izzard campaigns for the Labour In campaign for the EU referendum Christopher Furlong/Getty Images 16/34 Leader of the United Kingdom Independence Party (UKIP) Nigel Farage poses with the party's new EU referendum poster in Westminster Jack Taylor/Getty Images 17/34 CBI director general Carolyn Fairbairn, Rohan Silva, Chuka Umunna, Sarah Sands, Munira Mirza and MEP Daniel Hannan at the Evening Standard Brexit Debate Nigel Howard 18/34 The Vote Leave campaign bus passes a Vote Remain poster featuring Nigel Farage and Boris Johnson as it arrives for a visit to clothing and uniform manufacturers Simon Jersey in Accrington, Lancashire Stefan Rousseau/PA 19/34 David Cameron makes a joint appearance with Mayor of London Sadiq Khan as they launch the Britain Stronger in Europe guarantee card at Roehampton University Yui Mok/Getty Image 20/34 Prime Minister David Cameron recreates the famous Beatles Abbey Road album cover by walking across Abbey Road crossing with Tessa Jowell, former secretary of state for culture, media and sport, on May 20, 2016 in London, England. The Prime Minister is campaigning to 'Remain' in the European Union ahead of a referendum on June 23 to decide on whether or not to leave the European Union Jeremy Selwyn 21/34 Leader of the United Kingdom Independence Party (UKIP) Nigel Farage holds aloft a UK Passport as he speaks during an anti-EU campaign event in Birmingham AFP/Getty Images 22/34 Campaigners wear clothing bearing the slogans "I'm Turning My Back On The EU", and "I Want To Leave The European Union, Do You?" as they attend a an Anti-EU (European Union) United Kingdom Independence Party (UKIP) pro-Brexit campaign event, in Birmingham Paul Ellis/AFP/Getty Image 23/34 A British national receives her postal ballot paper AFP/Getty Images 24/34 Boris Johnson MP takes to the wicket during a visit to Chester-Le-Street Cricket Club as part of the Brexit tour Ian Forsyth/Getty Images 25/34 A campaigner with the pro-Europe campaign group called 'Irish4Europe', hands out leaflets to visitors to the London vs Mayo Gaelic Athletic Association (GAA) football game at Ruislip GAA grounds in Ruislip, northwest London AFP/Getty Images 26/34 Labour Leader Jeremy Corbyn and former leader Ed Miliband (L) address supporters and members of the public in Doncaster town centre on May 27, 2016 in Doncaster, England. The Labour In campaign battle bus arrived in Doncaster today with Labour leader Jeremy Corbyn and Ed Miliband MP to canvass for votes and hope to persuade UK citizens to stay in the European Union when they vote in the EU Referendum on the June 23 Christopher Furlong/Getty Images 27/34 Secretary of State for Justice, Michael Gove, leaves after attending a cabinet meeting at 10 Downing Street Carl Court/Getty Images 28/34 A Vote to Leave campaigner holds a placard as Leader of the United Kingdom Independence Party (UKIP) Christopher Furlong/Getty Images 29/34 The image of a sari-clad Asian woman exactly balanced on a see-saw with a shaven-headed "thug" was devised by advertising giant Saatchi and Saatchi for the Operation Black Vote campaign. OBV said the poster - which features the slogan "A vote is a vote" and is due to be displayed on 37 digital billboards in London and Manchester - highlighted the "demonisation of foreigners and people of colour" in the campaign 30/34 Two pumps of Fuller's London Pride are branded with 'IN' and 'OUT' labels in the Red Lion Pub in Westminster Dan Kitwood/Getty Images 31/34 People walk past a graffiti mural of Donald Trump and Boris Johnson kissing, which is sprayed on a disused building in the Stokes Croft area of Bristol. The image, called 'The Kiss of Death' and painted by pro-EU campaign group We Are Europe, highlights the upcoming deadline for voter registration for the referendum on 7th June Ben Birchall/PA 32/34 The front page of The Sun newspaper on 9th March The Sun 33/34 London Mayor Boris Johnson addresses supporters during a rally for the 'Vote Leave' campaign on April 15, 2016 in Manchester, England. Boris Johnson is taking part in a 48 hour 'Brexit Blitz' of campaigning in Northern England. Britain will vote either to leave or remain in the EU in a referendum on June 23 Christopher Furlong/Getty Images 34/34 John Whittingdale, Theresa Villiers, Michael Gove, Chris Grayling, Iain Duncan Smith and Priti Patel attend the launch of the Vote Leave campaign at the group's headquarters in London Stefan Rousseau/Getty Images 1/34 Boris Johnson (left) kisses a wild salmon as he is shown around Billingsgate Fish Market in London with porter Greg Essex, uncle of TV presenter Joey Essex, on the final day of campaigning Stefan Rousseau/PA 2/34 A van displaying an advert saying 'Don't Wake Up With Nigel Next Friday' is driven through Westminster Jack Taylor/Getty Images 3/34 Michael Gove speaks alongside Priti Patel (left) and Kate Hoey at a Vote Leave campaign event at Old Billingsgate market, London Dominic Lipinski/PA 4/34 A passenger on a train reads the Evening Standard on the London Underground EPA 5/34 Delia Smith during the Channel 4 EU referendum debate Dominic Lipinski/PA 6/34 David Cameron appears on a special referendum edition of BBC One's Question Time, hosted by David Dimbleby Stefan Rousseau/PA 7/34 Jayne-Anne Gadhia, CEO of Virgin Money, speaks to Sir Richard Branson about his views on the EU referendum Ben Pruchnie/PA 8/34 JD Wetherspoon beer mats that have been printed by the pub chain with strong messages in favour of leaving the EU JD Wetherspoon/PA 9/34 Ukip leader Nigel Farage and Kate Hoey on board a boat taking part in a Fishing for Leave pro-Brexit "flotilla" on the River Thames Stefan Rousseau/PA 10/34 Liberal Democrats leader Tim Farron greets supporters after arriving in the Liberal Democrat Vote Remain campaign bus in east London Ben Stansall/AFP/Getty Images 11/34 Boris Johnson MP visits Sam Cole Foods fish processing factory in Lowestoft, Suffolk, where he was campaigning on behalf of the Vote Leave EU campaign Stefan Rousseau/PA 12/34 A boat carrying supporters for the Remain in the EU campaign, including Sir Bob Geldoff, shout and wave at Brexit fishing boats as they sail up the Thames Ben Stansall/AFP/Getty Images 13/34 Yvette Cooper MP gives a helping hand to her husband and former shadow chancellor Ed Balls, as he gets up from a story time session, during a Vote Remain canvassing visit to Shadsworth Children's Centre in Blackburn. Christopher Furlong/Getty Images 14/34 The Sun backs Brexit Daniel Sotrabji/AFP Getty Images 15/34 Eddie Izzard campaigns for the Labour In campaign for the EU referendum Christopher Furlong/Getty Images 16/34 Leader of the United Kingdom Independence Party (UKIP) Nigel Farage poses with the party's new EU referendum poster in Westminster Jack Taylor/Getty Images 17/34 CBI director general Carolyn Fairbairn, Rohan Silva, Chuka Umunna, Sarah Sands, Munira Mirza and MEP Daniel Hannan at the Evening Standard Brexit Debate Nigel Howard 18/34 The Vote Leave campaign bus passes a Vote Remain poster featuring Nigel Farage and Boris Johnson as it arrives for a visit to clothing and uniform manufacturers Simon Jersey in Accrington, Lancashire Stefan Rousseau/PA 19/34 David Cameron makes a joint appearance with Mayor of London Sadiq Khan as they launch the Britain Stronger in Europe guarantee card at Roehampton University Yui Mok/Getty Image 20/34 Prime Minister David Cameron recreates the famous Beatles Abbey Road album cover by walking across Abbey Road crossing with Tessa Jowell, former secretary of state for culture, media and sport, on May 20, 2016 in London, England. The Prime Minister is campaigning to 'Remain' in the European Union ahead of a referendum on June 23 to decide on whether or not to leave the European Union Jeremy Selwyn 21/34 Leader of the United Kingdom Independence Party (UKIP) Nigel Farage holds aloft a UK Passport as he speaks during an anti-EU campaign event in Birmingham AFP/Getty Images 22/34 Campaigners wear clothing bearing the slogans "I'm Turning My Back On The EU", and "I Want To Leave The European Union, Do You?" as they attend a an Anti-EU (European Union) United Kingdom Independence Party (UKIP) pro-Brexit campaign event, in Birmingham Paul Ellis/AFP/Getty Image 23/34 A British national receives her postal ballot paper AFP/Getty Images 24/34 Boris Johnson MP takes to the wicket during a visit to Chester-Le-Street Cricket Club as part of the Brexit tour Ian Forsyth/Getty Images 25/34 A campaigner with the pro-Europe campaign group called 'Irish4Europe', hands out leaflets to visitors to the London vs Mayo Gaelic Athletic Association (GAA) football game at Ruislip GAA grounds in Ruislip, northwest London AFP/Getty Images 26/34 Labour Leader Jeremy Corbyn and former leader Ed Miliband (L) address supporters and members of the public in Doncaster town centre on May 27, 2016 in Doncaster, England. The Labour In campaign battle bus arrived in Doncaster today with Labour leader Jeremy Corbyn and Ed Miliband MP to canvass for votes and hope to persuade UK citizens to stay in the European Union when they vote in the EU Referendum on the June 23 Christopher Furlong/Getty Images 27/34 Secretary of State for Justice, Michael Gove, leaves after attending a cabinet meeting at 10 Downing Street Carl Court/Getty Images 28/34 A Vote to Leave campaigner holds a placard as Leader of the United Kingdom Independence Party (UKIP) Christopher Furlong/Getty Images 29/34 The image of a sari-clad Asian woman exactly balanced on a see-saw with a shaven-headed "thug" was devised by advertising giant Saatchi and Saatchi for the Operation Black Vote campaign. OBV said the poster - which features the slogan "A vote is a vote" and is due to be displayed on 37 digital billboards in London and Manchester - highlighted the "demonisation of foreigners and people of colour" in the campaign 30/34 Two pumps of Fuller's London Pride are branded with 'IN' and 'OUT' labels in the Red Lion Pub in Westminster Dan Kitwood/Getty Images 31/34 People walk past a graffiti mural of Donald Trump and Boris Johnson kissing, which is sprayed on a disused building in the Stokes Croft area of Bristol. The image, called 'The Kiss of Death' and painted by pro-EU campaign group We Are Europe, highlights the upcoming deadline for voter registration for the referendum on 7th June Ben Birchall/PA 32/34 The front page of The Sun newspaper on 9th March The Sun 33/34 London Mayor Boris Johnson addresses supporters during a rally for the 'Vote Leave' campaign on April 15, 2016 in Manchester, England. Boris Johnson is taking part in a 48 hour 'Brexit Blitz' of campaigning in Northern England. Britain will vote either to leave or remain in the EU in a referendum on June 23 Christopher Furlong/Getty Images 34/34 John Whittingdale, Theresa Villiers, Michael Gove, Chris Grayling, Iain Duncan Smith and Priti Patel attend the launch of the Vote Leave campaign at the group's headquarters in London Stefan Rousseau/Getty Images

Opinion was split 45-45 on another contentious claim that Turkey will be fast-tracked to EU membership, giving free movement rights to 75 million.

But the public reject Ukip leader Nigel Farage’s claim that there is a higher risk of sex attacks by migrants from staying in the EU: Just 28 per cent thought it true, 62 per cent said false.

Mr Cameron’s claim that the peace and stability of Europe would be put at risk by a Brexit was rejected by 59-32.

And the argument made by ex-premiers Sir John Major and Tony Blair that stability in Northern Ireland would be endangered was disbelieved by 61-21.

Even among Remain backers, more than half think the £4,300 figure is untrue.

Some 31 per cent thought their lives would be better in five years time if the UK leaves the EU.

Only 18 per cent thought they would be better off if Britain stays in the EU.

Neither side is much trusted.

Overall, only 19 per cent think politicians from both leave and remain are mostly telling the truth during the campaign.

Over twice as many, 46 per cent, think politicians are mostly telling lies.

If there was a general election, the poll found the Conservatives on 35 per cent, with Labour on 34, Ukip on 10 and the Lib Dems on nine.

Gideon Skinner, head of political research at Ipsos MORI, said: “The Leave campaign is getting their messages across, especially on the key public concern on immigration.

"But the Remain camp is finding it much harder to convince people that their core economic messages, both on the risks of Brexit and the benefits of staying, is going to have a personal impact on their lives.”

* Ipsos MORI interviewed 1,257 adults across GB by telephone from 11th – 14th June 2016. Data are weighted. Full details at www.ipsos-MORI.com