Defending his record on immigration and protecting the UK’s sovereignty, he said membership of the common market was vital to British businesses and claimed it would be “madness” to leave the 28-nation bloc to cut immigration.
Mr Cameron stuck by a pledge to reduce net migration to below 100,000 per year, despite missing the target ever since it was set.
He admitted that net migration from the EU over the course of his premiership had reached 600,000, but insisted his pledge could still be met despite the union’s free movement rules. However, he said he was “not going to put a date” on when that would be achieved.
The Prime Minister said: “I’ll be absolutely level with you, and the audience, and everyone back at home. We’re in the single market. It’s a market of 500 million people. It’s vital to the success of our businesses.
“Part of that single market is British people being able to work and live in other European countries and Europeans being able to come and live and work in our country.”
He later added: “If you want to get out of the single market, as the Leave campaign want to do, you will fundamentally damage our economy. That cannot be the right way of controlling immigration.”
Challenged by Sky News correspondent Faisal Islam over the ability of European courts to overrule British judges, Mr Cameron said there were times when the decision of the EU made him “crazy”.
He said: “If you’re saying there are frustrations, of course there are. We’re not having a referendum on do we approve every decision of the European court.
“We’re having a referendum on should we stay in this organisation which is good for our economy and strengthens Britain’s role in the world, or should be leave.”
Mr Cameron added that if the UK votes for Brexit, “we would have our nose pressed again the window” with no ability to influence the rules of the single market which businesses would be exporting into.
Under pressure during the initial interview, the Prime Minister repeatedly accused Mr Islam of being “glib” when challenging him on government warnings about the dangers of leaving the EU.
In response, Mr Islam provoked laughter from the audience when he asked: “What comes first, World War Three or the global Brexit recession?” The Prime Minister was also asked whether he had “reached for the classic Cameron scare campaign,” borrowing his tactics from the Scottish independence referendum.
Taking questions from a studio audience in the second half of the programme, Mr Cameron was repeatedly forced to defend his government’s decisions over investment in public services, as well as being grilled over the ability of Britain to succeed outside the EU.
At times audience members shouted over one another, and Mr Cameron was interrupted during one lengthy exchange over his support for Turkish membership of the EU.
“I’ve seen nothing but scaremongering, I’ve see no valid facts, I’ve seen no pros and cons,” said the questioner, Soraya Bouazzaoui, a student.
Following criticism from the Leave campaign and warnings of an influx of Turkish migrants, the Prime Minister dismissed Turkish accession as a distant prospect, replying: “At this rate they’ll join in the year 3000.”
Mr Cameron insisted that, if Britain was not a member of the EU, he would want to join under the terms he secured in the recent renegotiation.
He was also asked whether he thought his opponent in the Leave campaign and possible leadership challenger, Boris Johnson, would make a good Prime Minister, but declined to answer, saying only that he was “very talented” and had “fuel left in the tank”.
Sky News will adopt the same format this evening when it welcomes Michael Gove from the Vote Leave campaign.