Trust in David Cameron on the EU has collapsed at the same time as his Tory rivals in the Brexit campaign have gained popularity, a new poll reveals today.

Just 18 per cent of voters trust the Prime Minister on the EU referendum, showing his repeated warnings of a Brexit vote - known as 'Project Fear' - is failing to win over voters.

Boris Johnson is the most trusted politician on the EU with 31 per cent, with Labour leader Jeremy Corbyn second on 28 per cent.

It will bolster Mr Johnson's hopes of succeeding Mr Cameron soon after the June 23 referendum regardless of the result.

The YouGov poll for The Times shows the EU referendum result on a knife-edge, despite two polls in the last fortnight showing big leads for the campaign to Remain in the EU.

Trust in David Cameron on the EU has collapsed at the same time as his Tory rivals in the Brexit campaign - Boris Johnson and Iain Duncan Smith - have gained popularity, according to a YouGov poll for The Times

According to today's poll, both the Brexit and Remain campaigns are on 41 per cent, with 13 per cent undecided and 4 per cent saying they would not vote in the June 23 referendum.

On the issue of trust, even former Tory leader Iain Duncan Smith, another leading member of the Vote Leave campaign, is more trusted than Mr Cameron.

The Prime Minister's ratings have fallen by 3 per cent since last month - a period in which he has warned that Brexit would be the 'self-destruct option' that would send Britain into the worst recession since the credit crunch, make families worse off by up to £4,300 a year, add £230 a year to family holidays and warned that Europe could descend back into war and genocide.

The poll finds that since negotiating his EU deal in February, the public's trust in Mr Cameron has fallen by a remarkable 11 per cent - suggesting voters do not believe the Prime Minister's claim that his reforms give Britain a 'special status' in the EU.

The YouGov poll for The Times shows the EU referendum result on a knife-edge, despite two polls in the last fortnight showing big leads for the campaign to Remain in the EU

CAMERON BRANDED A COWARD FOR DODGING TV DEBATES David Cameron (pictured arriving in Japan today) was branded a coward last night for refusing to debate on TV with Brexit campaigners David Cameron was branded a coward last night for refusing to debate on TV with senior Brexit campaigners. Despite claiming the case to stay in the EU is overwhelming, the Prime Minister will take part only in interviews and question and answer sessions with voters. His opponents suspect he fears a clash over open borders when thousands of migrants are heading across the Mediterranean to Europe. EU border officials say a deal with Turkey to control the flow into Greece is working – with numbers down 90 per cent. But yesterday Italy said it had rescued more than 2,600 migrants from the sea in just 24 hours. The overwhelming majority were searching for a better life rather than fleeing war or persecution. Iain Duncan Smith accused the Government of trying to fix the June 23 referendum and stifle debate. ‘The refusal to engage in a fair contest is the definition of cowardice,’ said the Leave campaigner and former cabinet minister. ‘It must not be up to politicians to decide what the public sees and hears. It’s clear as day that this government is doing its level best to gerrymander the referendum and stifle debate. ‘Not only have they published reports that they brazenly admit are biased, and colluded with big business to bully staff into voting their way, they are now dictating the terms of public debate – selecting their own opponents and refusing to engage with those they deem too tough.’ Official immigration figures out tomorrow are expected to make grim reading for Mr Cameron – and confirm it is impossible to keep his promise to cut net immigration to below 100,000 while remaining within the EU’s free movement rules. Mr Cameron has now dodged a confrontation with Justice Secretary Michael Gove and ducked the chance to take on former London mayor Boris Johnson in the final TV showdown – a BBC-hosted debate 48 hours before polling day. Defence secretary Michael Fallon may now take his place. No 10 is said to have issued an ultimatum to broadcasters, warning that Mr Cameron would rather sit out their programmes than debate the merits of the EU with a senior figure from the Brexit camp on live TV. Advertisement

Mr Johnson's high popularity comes after he has taken a more prominent role in the Vote Leave campaign after stepping down as Mayor of London earlier this month.

He has spearheaded the Brexit campaign by meeting voters across the south west and Yorkshire on the Vote Leave battle bus.

But he has come under fire after comparing the EU's expansionist ambitions to Hitler's attempts to dominate Europe in the 1930s and was also criticised for delivering rants about banana regulations as Mr Cameron and Chancellor George Osborne presented sober economic warnings on Monday.

Despite this, a third of voters believe that he would be up to the job of being prime minister, according to the YouGov poll, compared to 11 per cent who say the same about Mr Osborne - his main leadership rival.

Even 22 per cent of Labour voters and three in ten Lib Dem supporters believe Mr Johnson would be a good prime minister. 57 per cent of Ukip voters believe the same.

According to the poll, one in five voters view Mr Johnson as a 'natural leader' whereas just 2 per cent see Mr Osborne in the same way.

Ukip leader Nigel Farage is also more trusted than the PM, on 22 per cent - ahead of pro-EU Theresa May and pro-Brexit Michael Gove on 17 and 16 per cent respectively.

But despite his low trust ratings, Mr Gove has been chosen to represent the Vote Leave campaign in two TV showdowns on the EU.

He will appear in a one-hour Sky News debate on the referendum next Friday - 24 hours after Mr Cameron, and the Justice Secretary will also face a live audience in BBC Question Time specials on June 15.

Four days later the Prime Minister, his close friend, will face the same challenge - on Sunday 19 in Milton Keynes.

But the pair will not go head-to-head in either the Sky or BBC events. Mr Cameron has been branded a coward for refusing to debate on TV with senior Brexit campaigners.

The dire trust ratings for the Prime Minister suggest he could be forced out of Number 10 earlier than he hoped.

A Leave vote on June 23 would almost certainly spell the end of his premiership but with fledgling confidence among voters and an increasingly hostile parliamentary party, he could even be pushed out after a Remain vote.

Mr Cameron has already pledged not to stand for a third term as PM.

Many in the party predict that a pro-Brexit MP will be the next leader even after a vote to stay in the EU in a bid to heal the wounds after months of infighting.

In the Conservative leadership contest Tory MPs choose the two candidates they want to be put forward for a vote by all Conservative members.

Senior figures in the party predict the two candidates could both be from the Eurosceptic wing of the party.

Today's poll finds a big divide between Conservative and Labour supporters, with just 35 per cent of Tory 2015 general election voters saying they will vote to stay in the EU but 70 per cent of Labour voters saying they back Remain, while 72 per cent of Lib Dem supporters say they will do so.

It paints a very different picture to a poll published yesterday, which found a majority of Tory voters are deserting Brexit.

An ORB poll for the Daily Telegraph found 57 per cent of Conservative voters are backing Remain compared to 40 per cent for Brexit. This was a complete reversal from its poll two months earlier, which showed it was Brexit that had a 13 per cent lead among Conservative supporters.

Yesterday's survey also found a majority of other previously core Brexit voters - pensioners and men - were now backing Remain.

The PM's ratings have fallen by two per cent since last month - a period in which he has warned that Brexit would be the 'self-destruct option' that would send Britain into the worst recession since the credit crunch, make families worse off by up to £4,300 a year and warned that Europe could descend back into war and genocide. Yesterday he visited Luton Airport (pictured) to warn Brexit could add £230 a year to family holidays

Boris Johnson (pictured waiting for a train at York station on Monday) is the most trusted politician on the EU with 31 per cent

THE APOCALYPSE IS COMING! IF YOU BELIEVE BOTH SIDES WHATEVER THE RESULT ON JUNE 23 WE'RE ALL DOOMED David Cameron has warned of war and recession during the referendum campaign David Cameron and George Osborne have warned Brexit would be the 'self-destruct' option for Britain as they unveiled forecasts the nation's economy would be plunged into a recession immediately by a vote to quit. IMF Chief Christine Lagarde said the consequences of an 'out' vote ranged from 'bad to very bad', with nearly 10 per cent potentially being wiped off the economy. Labour's former deputy leader Harriet Harman suggested leaving the union could boost sexism. She said Brussels had been a 'strong friend' to women and a vote to quit the union would be a 'major step back' in the fight for gender equality, she argued. David Cameron suggested that leaving could trigger another war in Europe in remarks that provoked a major backlash. Highlighting the sacrifice of UK forces in the Second World War, the Prime Minister said the 'risk' of another conflict should not be ignored. 'Can we be so sure that peace and stability on our continent are assured beyond any shadow of doubt?' he said 'The Bank of England governor also raised the prospect that Brexit could push the economy into recession. Mark Carney took the unusual step of saying it was 'possible' that UK growth could shrink after a vote to leave on June 23 as he warned of years of market turmoil. Boris Johnson enraged the Remain campaign to claim the EU had the same goal as Hitler Vote Leave have repeatedly claimed quitting the EU would save Britain £350million every week that it could instead spend on other priorities - such as the NHS. But the claim has been repeatedly dismissed as untrue by the Remain campaign and Sir Andrew Dilnot, of the UK Statistics Authority, said it was 'potentially misleading' because it ignored the rebate. The official Out campaign claimed polling in Turkey found 12 million of them would want to move to the UK if they were handed free movement. The campaign suggested the migration would also lead to far higher numbers of criminals travelling to Britain while Tory MP David Davis said an influx of Turkish workers would drive down wages. Boris Johnson claimed the European Union wanted the same goal as Adolf Hitler - but was pursuing it via 'different methods'. The ex-London Mayor said the dream of a European superstate was a flawed attempt to reclaim the golden age of the Roman empire in Europe. Out campaigners have insisted remaining in the European Union - and particularly the jurisdiction of the European Court of Justice - makes it impossible for Britain to secure its borders against terrorists. They claim free movement rules mean suspects can walktz into Britain unopposed. Advertisement

Knives out for Cameron: Dozens of Tories threaten no-confidence vote over PM's 'shabby' Brexit scaremongering

Dozens of Tory MPs are threatening to topple David Cameron over his handling of the EU referendum.

In the wake of the latest Brexit ‘dodgy’ dossier row, senior party figures said he would have to name a date for his departure if he wanted to avoid a massive bloodletting.

They said even this might not prevent a formal vote of no-confidence after June 23, whatever the poll result.

The plotting followed another day of extraordinary clashes between senior Tory party figures over No 10’s Project Fear strategy. Boris Johnson claimed a Treasury dossier was a ‘hoax’.

The knives are out: Dozens of Tory MPs are threatening to topple Prime Minister David Cameron (pictured yesterday with Chancellor George Osborne at an In campaign event in Chandler's Ford, Hampshire) over his handling of the EU referendum

Other Leave campaigners said the report was ‘disreputable, shabby and misleading’. The dossier claimed that up to 820,000 jobs would be lost, house prices would plunge and the country would dive into recession.

Some backbenchers were so enraged with Downing Street that they said a vote to try to get rid of the PM was now inevitable.

They pointed out that only six months had passed since Mr Cameron had declared there was ‘no question’ that Britain could survive and do well outside the EU.

Under Conservative Party rules, 50 MPs have to write to Graham Brady, the chairman of the backbench 1922 Committee, to trigger a formal no-confidence vote.

MPs say some letters have already been written – and dated June 24.

One senior backbencher said: ‘If there is a narrow win for Remain, and he is still in office after June 23, the only way he is going to avoid a vote of no-confidence is to name the date when he is going to go.

‘If he says that, while he still has much work that he wants to do, he will be gone by the end of 2018 then that might head off some of the opposition.

Former London Mayor Boris Johnson (pictured yesterday at a Vote Leave campaign event) claimed a Treasury dossier warning of 820,000 job losses in the event of Brexit was 'a hoax'

Former Defence Secretary Liam Fox called the Treasury dossier 'shabby and misleading'

'People want a date when they know that he will be gone. There is real anger.’

In a joint press conference yesterday, the Prime Minister and Mr Osborne claimed Britons would be voting to ‘self-destruct’ by backing Brexit on June 23.

Mr Cameron warned of a ‘DIY recession’ – one that the country would have brought upon itself.

But the Treasury dossier, which failed to consider any of the downsides of staying in the EU, was savaged by former Tory chancellors, serving ministers and MPs.

Mr Johnson said: ‘I see no evidence whatever there will be a recession, I really don’t. It’s totally made up and I think it’s started to be excessively negative and I think they are in danger of talking this country down.’

The dossier said in a worst-case, ‘severe shock’ scenario exit could result in 6 per cent lower GDP over two years, 820,000 lost jobs, a four per cent fall in average incomes, a 15 per cent collapse in the pound’s value and £39billion added to government borrowing.

In the lesser ‘shock’ scenario, based on assumptions of a bilateral trade deal with the EU, it predicts growth would be 3.6 per cent less than currently predicted in the two years after a British exit.

Sterling would drop 12 per cent, unemployment would rise by 520,000, wages would be hit by 2.8 per cent and house price growth would take a 10 per cent hit.

Former defence secretary Liam Fox said the analysis was ‘disreputable, shabby and misleading’ propaganda. Marcus Fysh, the Tory MP for Yeovil, tweeted that the Treasury analysis was ‘specious b******s’.

MEETING GEORGE PERSUADED ME...TO VOTE FOR BREXIT A B&Q worker said that meeting George Osborne yesterday had persuaded her to vote in the EU referendum – but for Brexit. The woman said she told the Chancellor he was not living ‘in the real world’ after listening to his speech warning that leaving the European Union would lead to a ‘DIY recession’. The employee, named only as Maryann, took a selfie with Mr Osborne before saying she would now vote to leave. Her comments came after B&Q workers were banned from talking to journalists at the event, sparking comparisons with a ‘totalitarian state’. B&Q worker Maryann, pictured with George Osborne, said meeting the Chancellor persuaded her to vote for Brexit over his 'stage managed' speeches Maryann, who described herself as an immigrant living in Leatherhead, Surrey, told LBC the speeches were ‘stage-managed’ and claimed she had been unable to ask the Prime Minister and Chancellor a question because they had their backs to her. She even claimed they should not have bothered visiting the firm’s offices, where she said a ‘majority’ back Brexit. She said Mr Osborne said she ‘shouldn’t believe anything the Leave campaign says’. But Maryann added: ‘What they have done is tip me over to the Leave side.’ Last night B&Q said Maryann had spoken out in a personal capacity, not as an employee. Advertisement

The smallprint of the dossier revealed that rather than collapsing, house prices and wages would roughly flatline.

The claim that Britain would spend a year in recession was based on four quarters of negative growth of just 0.1 per cent, which would be one of the shallowest downturns in history.

Even SNP leader Nicola Sturgeon, who is on the same side of the debate as Mr Cameron, said the warnings were overblown.

The Chancellor struck an unrelentingly gloomy tone, saying jobs would be lost in every region, with the message ‘Vote Leave, get recession’.

He also appeared to take a swipe at Michael Gove and Mr Johnson – accusing them of being prepared to sacrifice British jobs.

He said: ‘To those fellow politicians who say we should vote to leave I’d say this: you might think the economic shock is a price worth paying.

‘But it’s not your wages that will be hit, it’s not your livelihoods that will go, it’s not you who’ll struggle to pay the bills.’

Mr Cameron even suggested that voting for Brexit was immoral.

The Prime Minister said: ‘The economic case is the moral case. The moral case for keeping parents in work, firms in business, the pound in health, Britain in credit, the moral case for providing economic opportunity rather than unemployment for the next generation.

‘Where is the morality in putting any of that at risk for some unknown end?’

Tory MPs were so angry that a Treasury minister was hauled to the Commons to answer an urgent question on the dossier.

Senior backbencher Bernard Jenkin said: ‘We all know these forecasts are just rubbish’.

Cabinet minister Chris Grayling said that it was nonsense to claim Britain would be unable to strike trade deals outside the EU.

Nigel Lawson said: ‘The Treasury has enough trouble with forecasts even when they are trying to get them right. This time they have simply assumed a disaster in order to scare the pants off the British people.’

His fellow former Tory chancellor, Norman Lamont, said: ‘The Chancellor claims house prices will fall by 10 per cent by 2018 if the UK votes to leave, but the independent OBR forecasts that by 2018 house prices will be 10 per cent higher than now – so the Chancellor is claiming a vote to leave would mean stable house prices.’

Brexit-supporting economist Patrick Minford said the assessment ignored all the upsides from leaving, including the money saved from not having to abide by EU rules and regulations.

Mr Osborne said his analysis had been peer-reviewed by Charlie Bean, a former deputy governor of the Bank of England, and the economist had said it was based on reasonable estimates and best practice.

Leaving the EU could extend the government's austerity drive by TWO YEARS, think-tank warns

Britain could face two more years of austerity if it votes to leave the EU, according to a respected think-tank.

A sharp slowdown in the economy would probably force ministers to extend cuts and tax rises, the Institute for Fiscal Studies (IFS) said.

The curbs would be needed despite an extra £8 billion a year being freed up by no longer making contributions to Brussels.

But Vote Leave campaigners dismissed the IFS as a 'paid-up propaganda arm of the European Commission'.

The think-tank's report surveyed a range of forecasts about the economic consequences of cutting ties with the EU.

David Cameron and George Osborne have been pushing through austerity measures to eradicate the deficit since coming to power in 2010

It calculated that public finances would take a £20 billion to £40 billion hit in 2019/20, due to gross domestic product (GDP) being 2.1 per cent to 3.5 per cent lower than it would have been.

Paul Johnson, IFS director and an author of the report, said: 'Getting to budget balance from there, as the Government desires, would require an additional year or two of austerity at current rates of spending cuts.'

The IFS said Britain could use its contribution to the EU - estimated at £8 billion a year - to help shore up its finances if it voted for Brexit.

But it said this could be overshadowed by the negative impact on the UK economy, with a 0.6 per cent fall in national income offsetting the benefits.

IFS chief Paul Johnson

It also dismissed claims that the UK would have an extra £350 million a week to spend if it headed for the European exit door, while stating that its £8 billion saving from leaving the EU would be halved if it followed in Norway's footsteps and joined the European Economic Area.

Carl Emmerson, IFS deputy director and co-author of the report, said: 'The precise effects of leaving the EU on the British economy and hence the knock-on impact on the public finances is uncertain.

'But the overwhelming weight of analysis suggests that the economy would shrink by more than enough to offset the positive effect on the public finances of the reduced financial contribution to the EU budget.'

The IFS report - funded by the Economic and Social Research Council's UK in a Changing Europe scheme - said a vote to leave would increase economic uncertainty in the short term, ramp up the cost of trade and make the UK less attractive to foreign investment.

It said that this trio of pressures could see borrowing come in more than £20 billion higher in 2019, if national income falls in line with NIESR's prediction of 2.1% drop over that period.

It found that the Government would have to find the equivalent of £5 billion of public spending cuts, £5 billion worth of savings from social security spending and roll out £5 billion worth of tax rises if it wants to balance the books by 2019/20.

Chancellor George Osborne has pledged to return the UK to a surplus by 2020, with the Office For Budget Responsibility forecast stating that the UK would have a budget surplus of £10.4 billion in 2019/20 and £11 billion the year after.

Labour Shadow Chancellor John McDonnell said: 'The analysis from the IFS further underlines what a disaster it would be for the UK to risk a Tory Brexit under the Chancellor's recovery built on sand.

'We all know that the Tories want to use Britain leaving the EU as a pretext to slash workplace protections, but things could be even worse if a Tory Brexit led to even more austerity to try and meet George Osborne's self-imposed and self-defeating deficit targets.'

Patrick Minford, co-chair of Economists for Brexit, said: 'The IFS analysis acknowledges that the unilateral free trade approach recommended by Economists For Brexit would be the best option for the UK following an exit from the EU.

'The IFS comments that it is 'politically difficult' to embark on this WTO path. Yet this is entirely irrelevant for what is an purely economic argument.'

Dr Gerard Lyons, fellow co-chair of Economists for Brexit, said: 'The IFS's forecasts follow directly from the economic growth numbers.

'If one has a more upbeat view of the economic outlook with Brexit, as the Economists for Brexit group does, then naturally the budget numbers improve considerably.

'The analysis from the IFS highlights how vulnerable UK finances are to any economic setback, but we could easily suffer such a setback remaining in the EU.'

Vote Leave dismissed the IFS as a 'paid-up propaganda arm of the European Commission' which could suffer a financial hit from Brexit.

'The IFS is not a neutral organisation. It would face an £800,000 deficit if we vote Leave,' the campaign said.