They suggest the Tories are in the lead in every region in England except London, the North-east and the North-west.
The lead is narrowing, however, polling experts warned, with hopes of a Tory landslide “looking rather thin”.
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This poll is further evidence that the Prime Minister’s hopes of winning a landslide majority are beginning to look rather thin
Professor John Curtice – Polling expert
The poll of 1,013 people from across Britain found Labour leader Mr Corbyn is most popular with 18 to 24 year olds, even though a quarter of voters in that age group don’t believe he can pay for pledges like scrapping tuition fees.
Twenty six per cent of under-24s said they didn’t know.
Overall, just one in three voters (32 per cent) believe Labour can afford its manifesto promises, with 47 per cent questioning Mr Corbyn’s accounting.
The public believes the Conservatives will deliver a better Brexit deal than Labour, says the survey
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The Tories are in the lead in every region in England except London, says the survey
Asked which party would get the best Brexit deal for Britain, 38 per cent said the Conservatives, compared with 21 per cent Labour. Just eight per cent thought Ukip, despite the crucial role played by the party in securing last June’s referendum.
Twenty two per cent of voters didn’t believe any party would get the right deal for Britain. Even in London, which voted overwhelmingly for Remain, 33 per cent thought Mrs May would get a better Brexit deal with Mr Corbyn on 24 per cent.
The poll found Mrs May becomes more popular the older voters get, with 55 per cent of over-65s planning to vote for her, even after her so-called U-turn on social care.
Despite Mr Corbyn promising to keep perks like the winter fuel allowance, just 20 per cent of pensioners plan to vote Labour.
The survey, carried out on Wednesday and Thursday, found more women plan to vote Labour (34 per cent) than Conservative (33 per cent).
However, men overwhelmingly prefer Mrs May, with 38 per cent planning to vote for her compared with 29 per cent who would vote for Mr Corbyn.
Just eight per cent thought Ukip, would get the best Brexit deal for Britain
Labour has a six-point lead over the Tories within the M25 where they are on 36 per cent but Mr Corbyn is most popular in the North-west where 46 per cent of voters support him compared to 24 per cent who back Mrs May. Labour is also seven points ahead of the Tories in the North-east, on 40 per cent.
The Conservatives have the strongest support in the South-east where 46 per cent of the public plan to vote for Mrs May compared with 22 per cent for Mr Corbyn – a lead of 24 points.
The Prime Minister is also more popular in the East Midlands where the Tories are 16 points ahead of Labour on 46 per cent.
They are also on course to win 46 per cent of the vote in the East Midlands, where they are 11 points ahead.
In the traditional Labour heartlands of Yorkshire and the Humber, Mr Corbyn is also well behind Mrs May on 31 per cent compared with the Tories’ projected 39 per cent vote share.
The picture in Scotland looks bleak for Labour, too, where Mr Corbyn has been pushed into third place behind the SNP.
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Jeremy Corbyn during a visit to Hackney Marshes Football Pitches, to highlight Labour's manifesto commitment to ensure 5% of the Premier League's television rights income is diverted to the grassroots game, during a General Election campaign
The picture in Scotland looks bleak for Labour, where Corbyn has been pushed into third place
The Scottish Nationalists are on 37 per cent, the Conservatives on 25 per cent and Labour trail on 15 per cent.
In a Sunday Express poll in April, the Conservatives were on 42 per cent and Labour on 26 per cent.
The latest figures show the Tories’ lead has slipped by three points and Labour has gained nine points. Support has waned for both the Liberal Democrats and Ukip, with Tim Farron’s party down two points on eight per cent and Paul Nuttall’s Ukip also down two on six per cent.
The Green Party’s popularity is flagging, down three points to three per cent. Nine per cent of the public said they plan to vote for none of the seven main parties, including the SNP and Plaid Cymru.
Polling expert Professor John Curtice, of Strathclyde University, said: “This poll is further evidence that the Prime Minister’s hopes of winning a landslide majority are beginning to look rather thin. On these kinds of numbers she can’t necessarily be sure that she will end up with an overall majority.
Latest poll puts Tim Farron’s Lib Dems down two points on eight per cent
“The Tories are just four points ahead. They won’t lose the election but they won’t signifi cantly increase their majority with a four-point lead either. It’s less than the seven-point lead David Cameron had two years ago.
“Theresa May set herself a very high target when she called this election. We are still a mountain away from the Labour Party being anywhere near the largest party.
"On average, the polls are putting the Tories eight points ahead but that level is only slightly higher than in 2015 so we cannot be sure she’s going to get a substantial overall majority.
“She needs to hope polls by ICM and ComRes which are putting the Conservatives 12 points ahead, are right and those which put her below seven points are wrong. If she gets a majority of around 40 then the reaction will be, ‘Well, we’ve survived, but was it really worth it?’ ”