Tesco has become the latest supermarket to warn over stockpiling as grocers ramp up contingency plans for a no-deal Brexit.
Chief executive Dave Lewis said ensuring uninterrupted transport of fresh food across borders was the "single biggest challenge" for supermarkets if the UK crashes out of the EU without a deal.
He said the group was making contingency preparations for a no-deal scenario, but was still in "wait and see" mode until the outcome of negotiations becomes clearer.
He said: "The biggest single challenge will be in a no-deal scenario and what happens with fresh food.
"The possibility of stockpiling fresh food is very, very limited".
He stopped short of confirming if Tesco was actively stockpiling, but said it was a possibility with dry food.
Plans to ensure that fresh food transport is not held up is "where all our attention will be in the lead-up" to Brexit, with contingency planning stepping up after Christmas if a deal is still not struck, he added.
The comments come after German discounter Aldi said on Monday, it had considered stockpiling food as part of its preparations for Brexit.
But its UK boss, Giles Hurley, said Aldi’s increased fresh food range would make this more difficult.
Brexit Secretary Dominic Raab said in July that the Government is making plans to secure food supply in the event of no deal being struck.
But he said it was "wrong to describe it as the Government doing the stockpiling", indicating that industry would need to take the lead.
Research last week revealed food retailers face a mammoth £9.3 billion cost in the event of a no-deal Brexit.
According to Barclays Corporate Banking, higher tariffs and customs costs could hit supermarkets and their supply chains hard.
The report also warned shoppers would take on some of the extra cost in the price of their groceries.
Without a deal, Barclays said food and drink from the EU would be slapped with an additional 27% tariff under World Trade Organisation (WTO) rules, compared with between 3% and 4% on non-food items.