Cameron comfortable with live eventspublished at 21:07 British Summer Time 2 June 2016
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Questions to Mr Cameron from the studio audience turn to security. One man is sceptical about whether the UK will be shut out of security discussions if it votes to leave.
Mr Cameron says he is not saying that but says that EU cooperation "does matter".He's sure "we would find a way" to get back into the security arrangements we have currently - but it would take time and effort. He backs the European Arrest Warrant and highlights its role in capturing one of the 2005 London bombers.
The Q&A comes to an end with a plea from the PM not to "roll a dice" on the future of "our children and our grandchildren": "Britain doesn't succeed when we quit," he says.
The next question from the studio audience is from Victoria, who is planning to move out of London because she can't afford the housing prices and is worried about entry-level jobs for her children.
Mr Cameron says the economy will keep growing if the UK stays in the EU but accepts more needs to be done to create the educated workforce that can do the jobs that are being created.
Single mother Victoria says her daughter wants to train to be a paediatric nurse but can't commit to a degree because of the tuition fees, among other costs. "You need to make it easier David," she tells the PM.
Mr Cameron concedes he's been "making some new friends" during the EU referendum campaign - among them former TUC chief Brendan Barber - but says he is happy to appear on a platform with people who agree with him about the need to remain in the EU.
He says Jeremy Corbyn made a "very strong speech" today about remaining in the EU.
He's also asked about "another former mayor of London", can he guess which one? "Ken Livingstone?", Mr Cameron jokes.
No, it's leading Leave campaigner and Conservative MP Boris Johnson. Would Boris make a good PM? Mr Cameron says that's not for him to say. "He's been a great mayor of London, he's got plenty of fuel left in the tank," he says - but adds it's for others to decide.
Asked a question on the steel crisis from the studio audience, Mr Cameron says "supporting our industries" is better when the EU works together.
Denise, from Essex is up next. She admits being "quite angry". She accuses the PM of "hypocrisy" for appearing with Labour's Sadiq Khan on the EU - having attacked him during the London mayoral campaign.
The PM says he thinks it is right to work with the elected mayor of London even though he disagreed with some of the people he shared platforms with in the past. "Some of these issues are bigger than politicians," he says.
On the Sky News Q&A, a former NHS nurse asks David Cameron about the "never-ending stream of people" arriving from Europe and pressure on public services. "The worst thing we could do for our NHS is to wreck our economy by taking ourselves out of the single market," the prime minister replies.
An audience member says: "You need to fund it [the NHS] .. it's time that you and your government went."
The PM repeats that "shrinking the economy" will not help the NHS and says the Greens, Labour and the TUC are part of a "broad coalition" backing the Remain campaign. Someone in the studio audience suggests it is the "establishment" backing Remain.
Another audience question for David Cameron: One young woman says "scaremongering" has dominated the campaign which has made voting to remain seem "worse". She's also unhappy about the prospect of Turkey joining the EU amid international concerns.
Mr Cameron says there is a "positive case" for staying in the EU. The young woman tells him he's "waffling" and demands he reassure voters that they are "safe from extremism" when the EU wants to work with Turkey. "There is no prospect of Turkey joining the EU for decades," the PM says. "It's not going to happen."
First question from the audience: Would Mr Cameron join the EU now, if the UK was not already a member? The PM says the UK has the "best of both worlds" in the EU as it has its own currency but is in the single market. It's not in the Schengen no-borders zone but UK citizens can move freely. He says his negotiation has "enhanced our special status".
He clarifies: "I would never have Britain join the euro."
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Appearing on Sky News, David Cameron says if he didn't listen to warnings about Brexit from the IMF, OECD, Bank of England and the TUC, he would not be doing his job. It's his last question from political editor Faisal Islam ahead of questions from a studio audience.
What comes first? World War Three or the global Brexit recession, Faisal Islam asks the PM - a reference to dire warnings from Mr Cameron about what could happen if the UK votes to leave the EU.
The words "World War Three" were not in my speech, says Mr Cameron. But he goes on to say that there have been two "enormous bloodbaths" in Europe in the past century and asks if we can be confident peace can be kept. "I think you are being incredibly glib about this," he tells Mr Islam.
Will he withdraw the claim that leaving the EU will cost families £4,300 each?, Sky's political editor Faisal Islam asks. The Treasury Select Committee has criticised the use of the figure.
Mr Cameron says that figure represents the loss to the country, divided by the number of households. If the country is poorer, families will be poorer he says.
Mr Cameron says negotiating new trade deals would take 10 years - Faisal Islam puts it to him there would be no change for two years, while exit negotiations took place.
The PM said the UK would then operate under WTO rules with 10% tariffs which would "hammer our farmers" and jobs.
The prime minister admits "frustrations" with the EU but says many of them were addressed in his negotiations with other EU leaders ahead of calling the referendum.
"We're not having a referendum on: 'Do we approve of every decision of the European court?'" he says.
He says he's not arguing the organisation is "perfect" but says he has secured deals for the UK that deal with some of the issues.
"Sometimes this organisation drives me crazy," he says.
But he says Britons are not "quitters" and the EU will not stop existing if the UK backs Brexit - instead the UK would be left with its "nose pressed to the window" trying to work out what decisions were being made in its absence.
Asked by Sky's political editor about the European Court of Justice overruling him on VAT for solar panels and wind turbines, David Cameron says the "main rate of VAT is within our control". He says the court does "from time to time" make rules about specific projects but says his pledges on the principle rates of VAT and income tax remain.
On the Sky News debate, David Cameron says getting out of the single market "will fundamentally damage our economy" which "cannot be the right way of controlling immigration".
Sky News political editor Faisal Islam suggests Mr Cameron made promises to reduce migration that were not achievable. Mr Cameron says he does need to do things to control it - like restricting welfare - but not by damaging the economy.
Faisal Islam puts it to him that he has failed to hit his targets on migration and failed to get a deal from the EU that would allow him to do so. The PM says he has to accept "a single set of rules" as part of the single market but says he achieved targets for cutting bureaucracy during his EU negotiations.
Mr Cameron says the "worst thing we could do" to tackle the "challenge" of migration is to pull out of the single market.
Faisal Islam suggests he cannot control the freedom of movement of people - Mr Cameron says it remains "the right ambition for Britain" to reduce immigration, as he pledged.
"There are good ways of controlling migration and bad ways," he says. The good way is to reduce unemployment benefits and make more stringent demands about new migrants working and paying "into the system" before getting welfare access.
First question in the Sky TV event with David Cameron is on the thorny issue of migration. Sky News political editor Faisal Islam asks about the net number of EU migrants that have arrived in the UK since Mr Cameron became PM in 2010. The PM replies that about 600,000 have left this country and about 1.2 million have come to live or work here. It's "big numbers moving in each direction", says the PM. He says it's a big challenge - but it can't be solved by leaving the single market and damaging the UK economy, as he sees it.
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