Household bills for food and clothing will rise by an average of £220 a year if we leave the EU, according to the Prime Minister.
It comes as four former high street bosses warn Brexit would lead to higher prices.
David Cameron warns of a "stark" situation with a 3% rise in the cost of food and a 5% increase in clothing prices if Britain separates its ties with Brussels.
In an article in the Sun On Sunday the PM quotes "independent analysts" predicting that if we leave the EU "the fall in the value of sterling would be an average 12%".
He writes: "Let's be clear what that means: a weaker currency means more expensive imports; that means more expensive food and it drives higher business costs; and we all know where that ends up: higher prices in the shops."
Mr Cameron later visited an Asda supermarket in Hayes with the Remain campaigner and former acting Labour leader, Harriet Harman.
He tweeted: "We are clear - prices will rise if we leave the EU. #StrongerIn."
In a similar vein, the former chiefs of Tesco, Sainsbury's, Marks & Spencer and B&Q say leaving the EU would have a devastating effect on the economy
In an article in the Mail on Sunday, Sir Terry Leahy of Tesco, Marc Bolland of M&S, Justin King of Sainsbury's and Sir Ian Cheshire of B&Q owner Kingfisher say: "We believe an exit could be catastrophic for the consumer recovery on which so much of our economic stability depends.
"It is impossible to see how there could be an exit without an impact on prices and inflation. The unintended consequences of a Leave vote and the uncertainty it would create would be a massive shock to the system."
Referring to new treasury analysis Mr Cameron predicts the average cost of the weekly family shop for food and drink would rise by almost 3% - £120 a year.
Clothing and footwear would see a 5% increase - an extra £100 a year for the average family.
In February the pound dropped 2% against the dollar, hitting a seven-year low, following the news that Boris Johnson had joined the Brexit campaign.
Two days later HSBC warned it could fall by a further 20% if Britain chose to leave the EU.
However, Out campaigners will see this latest report as another chapter in the Government's "project fear". They argue that the UK will continue to thrive outside of the EU as part of a free trade zone.
This latest intervention follows George Osborne's warning that people's homes would lose their value by up to 18% post-Brexit, prompting the former Work and Pensions Secretary Iain Duncan Smith to describe the Chancellor as "Pinocchio".
This is not the first time food prices have been used as an argument to remain. A study by the National Farmers' Union (NFU) in April made similar findings about food prices.
The new figures are separate to previous treasury analysis which suggested that in the long term families would be £4,300 worse off outside the EU, a figure that was blasted as "worthless" and "absurd" by Brexit campaigner John Redwood.
But the PM writes: "The evidence is clear: leaving the EU carries serious risks - to your job, to your wages, to the economic security that families rightly prize above all else. And as we show today, it would hit you in the wallet and at the checkout, too."
Matthew Elliott, chief executive at Vote Leave, said: "'The EU is good for the bosses and for the bankers. It isn't good for the public who have to pay the taxes that go to the EU instead of to our NHS and it isn't good for small businesses.
"As independent experts have found, the EU pushes up the prices in our supermarkets because of its protectionist policies. That's ok for big business fat cats but it's not good for British families."
:: Former acting Labour leader Harriet Harman and Justice Minister and Vote Leave campaigner Dominic Raab will be appearing on Sky News' Murnaghan show from 10am today.
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