George Osborne has blamed David Cameron for stoking Eurosceptic fears ahead of the EU referendum as he claimed everyone has “paid the price” for the former prime minister saying “Brussels was to blame”.

In a swipe at his long-time ally, the ex-chancellor said Mr Cameron was among a string of Tory prime ministers who had sought to blame the EU for problems at home.

Meanwhile, Mr Cameron himself said that a second EU referendum should not be ruled out, and hinted that he would again vote to Remain.

In a new BBC documentary lifting the lid on Mr Cameron’s premiership, Mr Osborne said he felt “responsible” for the Brexit chaos due to his role as chancellor, saying the referendum “should never have [been] held”.

He said: “I feel very sorry for what happened, and I feel responsible, I was the chancellor of the exchequer in that government.

“We held a referendum we should never have held, we then lost that referendum and the consequences for the country are grave and the only thing I can plea in my mitigation is that a huge number of people wanted that referendum, and I made a case against it, but it wasn’t heard.

David Cameron's premiership - in pictures Show all 15 1 /15 David Cameron's premiership - in pictures David Cameron's premiership - in pictures Britain's Queen Elizabeth II greeting David Cameron at Buckingham Palace for an audience to invite him to be the next Prime Minister on 11 May 2010 PA David Cameron's premiership - in pictures Prime Minister David Cameron and his wife Samantha wave from the steps of Number 10 Downing Street on 11 May 2010 Getty Images David Cameron's premiership - in pictures On 12 May 2010 Prime Minister David Cameron said in a press conference with Lib Dem leader Nick Clegg, who was then deputy PM, they plan to "take Britain in a historic new direction" and Conservative-led coalition government would be united and provide "strong and stable" leadership Rex David Cameron's premiership - in pictures A decade ago, David Cameron visited the Arctic to witness the effects of climate change. However since coming to power in 2010, his government has gradually dropped down a succession of green policies David Cameron's premiership - in pictures Prime Minister David cameron told the then New York mayor Michael Bloomberg, the Queen had “purred down the line” after he told her Scotland had voted against independence in September 2014. He was forced to apologise for breaking constitutional convention Getty Images David Cameron's premiership - in pictures Britain's Prime Minister David Cameron greeted soldiers working on flood relief in York city centre after the river Ouse burst its banks, in northern England in December 2015 REUTERS David Cameron's premiership - in pictures Claims that David Cameron performed an obscene act with a dead pig and smoked cannabis during his studies at Oxford University spread around the world in September 2015. The extraordinary allegations were made in an unauthorised biography of the Prime Minister written by Lord Ashcroft David Hartley/REX Shutterstock David Cameron's premiership - in pictures In 2016, Mr Cameron was caught up in a worldwide scandal dubbed the “Panama papers” Reuters David Cameron's premiership - in pictures Prime minister David Cameron and his wife Samantha with seven week old Regan as they meet her parents, first time home buyers Robert Arron and Kelly Jeffers at the Heritage Brook housing development in Chorley, Lancashire. David Cameron has joked that he wants "another baby" and said that he feels a "bit broody" every time he sees a newborn on the campaign trail David Cameron's premiership - in pictures Prime Minister David Cameron was criticised for branding refugees in the Calais ‘jungle’ camp as a “bunch of migrants” in January 2016 after thousands of refugees died in their attempt to cross the Mediterranean in 2015 Sky News David Cameron's premiership - in pictures Britain's Prime Minister David Cameron speaks with European Commission President Jean-Claude Juncker during an EU summit meeting on 17 March 2016 at the European Union council in Brussels. Cameron was in Brussels to renegotiate deal of UK membership with other European leaders. The deal, sealed after hours of haggling at a marathon summit, paved the way for a referendum on whether Britain will stay in the EU AFP/Getty Images David Cameron's premiership - in pictures President Barack Obama shakes hands with British Prime Minister David Cameron at a meeting at 10 Downing Street in London on 22 April 2016. The President and his wife visited 10 Downing Street where he joined press conference with British Prime Minister David Cameron and made his case for the UK to remain inside the European Union Getty Images David Cameron's premiership - in pictures After David returned from Brussels claiming victory in his renegotiation with European leaders, Boris Johnson announced that he will not support the Remain campaign. The prime minister said publicly he was "disappointed but Boris remains a friend" PA David Cameron's premiership - in pictures Prime Minister 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 on 20 May 2016 in London. The 'guarantee card' lists five pledges should Britain remain in the EU, including the protection of workers' rights, full access to the single market and stability for Britain David Cameron's premiership - in pictures Britain's Prime Minister David Cameron speaks outside 10 Downing Street on 24 June 2016. Cameron announced his resignation after Britain voted to leave the European Union after a bitterly divisive referendum campaign AP

“David Cameron was just one of a number of British prime ministers who had fed this idea that we were different than Europe, that Brussels was to blame and that the public ultimately had to have a say, and we’ve all paid a price for it in my view.”

Speaking to LBC radio’s Nick Ferrari, Mr Cameron said he would “go to my grave wondering” if he could have seen off the Leave campaign by getting a better deal in his renegotiation of Britain’s EU membership or delaying the referendum.

He was critical of Labour leader Jeremy Corbyn’s “lukewarm” support for the Remain campaign, saying: “I was on the battle lines fighting as hard as I could and sometimes I’d turn around and wonder where Jeremy Corbyn was.”

Mr Cameron said he felt “a lot of sympathy” for Boris Johnson when he ducked out of a press conference in Luxembourg this week for fear of being drowned out by protesters.

But he made clear his disagreement with the PM’s decision to rule out a second referendum, telling Ferrari: “I don’t think you can, because we can’t go on being stuck... We’ve got to have either a deal, an election or a referendum.”

He avoided stating explicitly which side he would back in a fresh poll, but hinted he would support Remain, saying: “You know my views... I think we’re better off fighting from the inside.”

In the BBC programme, Mr Cameron also admitted for the first time that he asked the Queen to intervene in the Scottish independence referendum amid serious concerns in Westminster over a potential victory for the Yes campaign.

The Queen told wellwishers outside a church in Aberdeenshire that she hoped people “will think very carefully about the future”, in what was widely perceived as a boost to the No campaign just days before the 2014 vote.

Mr Cameron revealed he had been staying at Balmoral, when a newspaper poll came out putting the Yes campaign ahead for the first time, which he compared to a “blow to the solar plexus”.

He said: “I remember conversations I had with my private secretary and he had with the Queen’s private secretary and I had with the Queen’s private secretary, not asking for anything that would be in any way improper or unconstitutional but just a raising of the eyebrow even you know, a quarter of an inch, we thought would make a difference.”

Of the remark, Mr Cameron said: “It was certainly well covered although the words were very limited, I think it helped to put a slightly different perception on things.”

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Both politicians also talked about their attempts to keep Michael Gove on their side during the referendum, with Mr Cameron describing his defection to the Leave campaign as a “bombshell”.

Speaking on the programme Mr Gove, said: “Some of the conversations we had were attempts on his part to reassure himself that our friendship would mean that I wouldn’t stray from the fold.

“I think David, understandably, felt that since I’d been prepared to knuckle under on a number of occasions beforehand and put my own feelings to one side in order to serve the team, that on this occasion, I would do the same.”

The revelations come on the day of publication of Mr Cameron’s long-awaited memoir, in which he laid into his former colleagues Boris Johnson and Mr Gove, and expressed remorse over the political chaos caused by the referendum result.

In the book, the former PM revealed that he considered scrapping the UK’s Trident nuclear missile system shortly after coming to power at the head of a coalition government in 2010.

With the government aiming to slash billions from the defence budget and Liberal Democrat coalition partners challenging the planned like-for-like replacement of the four-submarine Trident fleet, Mr Cameron publicly announced a “value for money” review of the programme.

But the memoir revealed that he also commissioned a secret report – known only to Mr Osborne, foreign secretary William Hague and defence secretary Liam Fox – to see whether a cheaper alternative could be found.

The report found that the most viable other option – cruise missiles, which can be launched from land, air or sea – was a “dead end”, and the Strategic Defence and Security Review of 2010 confirmed the government’s intention to press ahead with Trident on a delayed timetable and a reduced number of warheads.

“I wanted to prove to myself that Trident was the right option for us,” wrote Mr Cameron. “Very secretly, and with only the chancellor, foreign secretary and defence secretary knowing, I commissioned a report on the alternatives.

“And there was an alternative: cruise missiles tipped with nuclear warheads. The problem was that over their 40-year lifespan there was a risk that they would become comparatively slow as new defence systems were developed.

“They might have been less expensive than Trident, but by the time the tests had been done to see if they worked, they could well have cost the same or even more.