Exclusive: Prime minister claims protected NHS cash may have to go as he cautions voters on possible consequences of voting to leave

David Cameron has warned that pledges to raise state pensions every year and ringfence spending for the NHS may have to be ditched in a brutal new phase of austerity if the country votes for Brexit.

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With Downing Street increasingly anxious about levels of support for leaving the EU, particularly among Labour voters, the prime minister says people need to focus on the “cold reality” of what Brexit would mean to their everyday lives and what they value most.

In an exclusive interview with the Observer, with only 12 days to go until the crucial referendum vote, Cameron insists he is not trying to scare people but is focusing on the reality of what life would be like outside the EU and the world’s largest trading market.

He says the so-called “triple lock” that guarantees annual increases in state pensions, ringfenced spending on the NHS, free TV licences and bus passes for pensioners, as well as defence spending would all be under threat.

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The prime minister argues that a “black hole” in the public finances – predicted by the Institute for Fiscal Studies by 2020 in the event of Brexit – would threaten the very services that people cherish and rely on most.

Annual state pension increases are currently guaranteed by the triple lock, which ensures they rise in line with whichever is higher: earnings, inflation or 2.5%. But if Brexit happened this costly commitment would be in doubt.

“You would have to start cutting things that people really value, whether it is the money going to the NHS or whether it is support for our pension system, and that could mean reviewing the triple lock,” the prime minister says.

Cameron insists he fully intends to honour a commitment to increase NHS spending by £10bn by 2020 but adds: “If we leave, independent and respected experts like the IFS and National Institute for Economic and Social Research say that by 2020 we will face a black hole in our public finances of up to £40bn.

“In those circumstances, future funding for the NHS could be at risk. Our ability to ringfence and protect spending on health could be at risk, too. This is the cold reality of leaving the EU – that’s why doctors, nurses and the boss of the NHS all say we will be stronger, safer and better off in the EU.”

Senior sources in the Remain camp said Cameron’s remarks were part of a deliberate attempt to “nail the lie” being spread by the Leave campaign, headed by Boris Johnson and Michael Gove, that quitting the EU would free up money that could be spent on public services.

Remain says the impact on economic activity and, as a result, tax receipts into the exchequer would lead to a massive shock and new public spending cuts.

Cameron made clear that in the coming week leading Labour figures, including leader Jeremy Corbyn, London mayor Sadiq Kahn, former premier Gordon Brown and former home secretary Alan Johnson would be given centre stage in the remain campaign, so that they could appeal directly to Labour followers. He called on them not to use the 23 June vote as a chance to punish him or the Tories but to support what is a huge coalition from the left and right that is backing continued EU membership.

The vote was “more important than a general election”, Cameron said. He added: “They are voting for a generation, for a lifetime. It is about their children, and grandchildren. What I would say to [Labour voters] is, look at the scale, look at the range behind Stronger In. You have got the trade unions, Greens, the Lib Dems, Labour, a Conservative government. It is a very, very big coalition.”

The latest Opinium/Observer poll shows the result still too close to call, with Remain on 44%, Leave on 42% and those who say they don’t know how they will vote on 13%.

Leading analysts, such as Ian Harnett, chief investment strategist at Absolute Strategy Research, and a former top strategist at UBS, are also warning that sterling’s value could drop by 30%, to a point close to parity with the US dollar, and that the stockmarket could plunge by 20% in the event of Brexit.

Writing in the Observer, shadow chancellor John McDonnell says any new trade deals that the UK makes with other countries if it leaves the EU would lead to the dismantling of workers’ rights. “If we don’t fight to keep and expand the working rights we have at an EU level, then a Tory Brexit government will only negotiate them away in trade deals that will resemble TTIP [the Transatlantic Trade and Investment Partnership] on steroids,” he says.

In the Observer interview, Cameron describes claims by his justice secretary, Michael Gove, that the country has had enough of hearing from economists and other experts as “absurd”. He says that the leave lobby is in danger of “morphing into the Little England campaign” of Ukip leader Nigel Farage, which wants to take the country backwards to the days when it was the “sick man of Europe”.