But the PM’s latest salvo in the increasingly bitter referendum battle is likely to intensify allegations of scaremongering from the Leave camp, which strongly disputes the Whitehall calculations over the economic cost of Brexit.
Speaking at the Luton HQ of low-cost airline EasyJet, Mr Cameron drew on analysis by the Treasury suggesting a 12 per cent slump in the value of the pound against the euro if the UK votes to quit the EU in the 23 June referendum.
According to government calculations, by 2018 the weaker pound will mean four people on a nine-night break to Spain could pay £225 more, with eight nights in France up £210, a fortnight in the US up £620 and ten nights in Portugal costing £325 more.
Mr Cameron told airline workers: “If we were to leave, and the pound were to fall – which is what most people expect and what the Treasury forecast – that would put up the cost of a typical holiday for a family of four to a European destination by £230.
“It could put up the cost of air travel, because if you are outside the single market … then you would face all sorts of bureaucracy and restrictions that you don’t face today.
“Another very retail thing that is happening in Europe is we are abolishing[mobile phone] roaming charges in the European Union. It’s one of the most annoying things – you’re on holiday, you use your mobile phone, you get an enormous bill. Getting rid of roaming charges could mean on a ten-minute call back to the UK, you’re saving almost £4.
“I think there are some very strong retail arguments about the cost of a holiday, the cost of food, the cost of using your phone, for staying in the European Union.”
But Mr Cameron insisted he was not offering a “head against heart” trade-off, in which the economic case for Remain is pitched against the patriotic appeal of Leave.
Staying in the EU was the patriotic thing to do, he said, because Britain’s strength and standing in the world were enhanced by its membership of international bodies.
“I think the big, bold, patriotic case is to stay in a reformed European Union to fight for the sort of world that we want, rather than to stand back and be on the outside.”
Mr Cameron’s former policy guru Steve Hilton, who backs Brexit, said the holiday price warning was another example of the sort of “pathetic, patronising EU scares” being deployed by both sides.
“You’ve got to be kidding. It’s almost like a parody,” he said. “I just wish we could have a serious debate about the long-term future of how we want to be governed rather than this kind of nonsense. It just does not do anyone any favours. It just puts people off the whole political class.”
Carolyn McCall, chief executive of EasyJet, said it was “highly likely” that fares would rise if the UK left the EU.
On roaming charges – which have been cut and are set to be abolished from June 2017 – No 10 was backed by BT Group chief executive Gavin Patterson and Vittorio Colao, chief executive of Vodafone Group. Both also said remaining in the EU would be better for their firms and for UK jobs.
Mr Cameron’s latest offensive came amid a furious response from eurosceptic Tories to Monday’s Treasury analysis which warned that Brexit would plunge the UK into a year-long recession and cost up to 820,000 jobs.
Reports have circulated that Tory MPs were planning a vote of no confidence in the Prime Minister after the referendum.