The Conservative leader and Labour MP met staff at a branch of Asda in west London and walked side by side down the store's cereal aisle before the shop officially opened for the day, The Press Association reported.
Mr Cameron claims a vote to leave the EU would mean the average family would pay out an extra £123 a year on food and drink, while an extra £98 would be spent on clothes and footwear.
Asked if Labour leader Jeremy Corbyn was supportive of her supermarket engagement with Mr Cameron, Ms Harman said: "Oh yes, because we are very worried about the implications, what would happen, if we were to leave the EU.
"And I think really the last thing anybody wants is their food prices to go up.
"And that's even more an issue if you're a household on quite a low income, then the food costs are a big part of your weekly bills.
"So going out of the EU, especially when so many of our goods come from the EU, it would increase people's food prices."
Ms Harman said it is "blindingly obvious" that leaving the EU - which she said would cause a "big economic shock" - would hit the value of the pound and imports will cost more.
"I mean it's a no brainer," she said.
Ms Harman was asked if she thought the Leave campaign could cause racial tension, following their claims that Britain will open the doors to high levels of murderers and terrorists from countries like Turkey if it remains in the EU.
"I think that they're throwing out an awful lot of speculation when we think that they should be focusing on the basic issues of jobs and prices.
"I mean there's been a suggestion that Turkey would be joining the EU, and then immediately everybody from Turkey would be coming to live in the UK.
"But even the EU itself says that there's no question of Turkey joining. And even if there was a question of that, we would be able to veto it.
"So I think that that is scaremongering," she said.
Ms Harman and Mr Cameron's first stop in Asda was in the fruit and vegetable section, before they made their way via the cereal aisle to a staff room.
The Treasury took the average of estimated depreciations (12%) in sterling following a vote to leave in a bid to show the impact on prices after two years.
It said food and drink would change by 2.9%, while clothing and footwear would go up by 5%.