The Prime Minister says Treasury analysis on the dangers of leaving the EU will mean food prices will go up three per cent while clothing and footwear will rise five per cent.
That would add £120 a year to the average family's food shop and another £100 for clothes and shoes.
The PM's claims were backed up by former bosses of Tesco, Sainsbury's, M&S and B&Q, who today claimed Brexit will cause a "massive shock" that drives up prices of imported goods.
Sir Terry Leahy, Wyevale Garden Centres owner Terra Firma vice president Justin King, Marc Bolland and Sir Ian Cheshire wrote: "We have had the privilege of leading some of Britain’s largest and most successful retailers. Over the past 20 years, retail has been through a phenomenal transformation and remains one of the most dynamic and innovative industries in the UK.
"Consumers have never had such a large range of choice and quality. They can shop 24 hours a day, either in stores or online, at prices more affordable than ever. This has all been achieved with Britain as part of the European Union.
"Like the Leave campaigners, we believe Britain is a truly world-class country. But unlike them, we believe an exit could be catastrophic for the consumer recovery on which so much of our economic stability depends.
"It is impossible for us to see how there could be an exit without an impact on prices and inflation, the strong relationships we’ve built with our EU supplier partners, and the broader innovation and digital agenda.
"The unintended consequences of a Leave vote and the uncertainty it would create would be a massive shock to the system. It would probably mean further depreciation of the pound, driving up the price of imported goods for consumers.
"In the UK we have strong and sophisticated supply chain relationships across Europe, integrated in a way they never were in the past. At the moment there are no barriers to trade within the EU. In trading with the rest of the world, all sorts of rules and tariffs get in the way.
"A vote to exit would necessitate a complete renegotiation of our trading arrangements, which can only be of detriment to UK consumers. We can also expect our trading partners to exploit this renegotiation to their benefit. It’s difficult to imagine French farmers will continue to allow British lamb to be freely imported.
"This leads to questions over the future of British agriculture as well as food manufacturing – an industry in which we are net exporters – and therefore the ultimate impact on jobs.
"There is no guarantee we can renegotiate quickly and efficiently enough to deal with some of these issues. As large retailers, our experience over many years is that scale gets you a better deal and being under time pressure is never helpful.
"British retail’s advancement over the next ten years is heavily reliant on investment in digital technology. The EU’s recently agreed Digital Single Market strategy will open up opportunities for business and consumers across Europe, making the single market fit for the digital age.
"Britain is the digital hub of Europe and has led the way in shaping the digital economy. Indeed, this country is the e-commerce capital of Europe, with a market share of over one third. We have the expertise to continue to lead and it would be a massive missed opportunity to leave the EU now and not be part of the broader revolution.
"Finally, there is the issue of regulation. The much-cited suggestion that we will be free of the apparent constraints of over-regulation if we leave Europe is nonsense.
"We need regulation to protect consumers and, if we want to continue to trade with Europe, the rules still apply. If we left, there is the risk that Westminster would continue to build additional regulation on top of the European laws, making it more onerous rather than less. So it makes much more sense to have a seat at the table to shape future regulatory change rather than simply be bound by it.
"There is no doubt this is a fundamental decision for the British people. While we are not advocates of scaremongering, it is just good business to understand the risks before reaching a conclusion in this complex debate. We have a responsibility to help inform the consumers we have served for many years.
"While the EU is by no means perfect, exit would hit consumers the hardest. For that reason we will be voting to stay and continue to play our part in the successful and growing Europe we all want to see."