Tesco has become the latest supermarket to place limits on the number of items shoppers can buy, following a similar move by rival Morrisons.
It now has a three-items per customer limit on flour, dried pasta, toilet roll, baby wipes and some wet wipes.
The supermarkets are acting to prevent a repeat of the panic-buying that led to shortages in March.
The managing director of Iceland told the BBC he is urging shoppers to "calm down and carry on as normal".
Richard Walker said his supermarket chain was not currently considering limiting purchases on any lines. He said there had been a small uptick in interest in the "usual suspect products" like toilet roll, but it was "nothing like last time".
Mr Walker said that, in March and April, this had resulted in elderly and vulnerable people, as well as NHS workers, being faced with empty shelves. He described panic buying as socially divisive, only an option to those who can afford it.
Tesco said it had "introduced bulk-buy limits on a small number of products".
It said this was to "ensure that everyone can keep buying what they need".
"We have good availability, with plenty of stock to go round, and we would encourage our customers to shop as normal," it said.
The supermarket has introduced additional limits for a small number of products online, such as rice and canned veg.
Morrisons introduced a limit of three items per customer on some ranges on Thursday, including toilet rolls and disinfectant products.
It said stock levels "were good", but it wanted to "make sure they were available for everyone".
In March, UK supermarkets were forced to take steps to prevent shoppers from panic-buying around the height of the pandemic.
Many introduced limits on the number of certain items that customers could buy, such as flour, pasta or toilet roll.
Enhanced measures introduced in recent weeks have not triggered stock-piling by customers, according to several supermarkets approached by the BBC earlier this week.Tesco joins Morrisons to limit sales of some items
Asda said it still had good availability in-store and online, while Waitrose said it had "good levels" of stock and that it had also looked at the items people bought early in lockdown and planned ahead accordingly.
"We would like to reassure customers that there is no need to worry about buying more than they need," a spokesperson said.
The British Retail Consortium said supply chains were good and has urged consumers to "shop as you normally would".
Director of food and sustainability at the BRC, Andrew Opie, said: "Supply chains are stronger than ever before and we do not anticipate any issues in the availability of food or other goods under a future lockdown.
"Nonetheless, we urge consumers to be considerate of others."
Aldi boss Giles Hurley has written to customers saying: "There is no need to buy more than you usually would. I would like to reassure you that our stores remain fully stocked and ask that you continue to shop considerately."