London's Metropolitan Police said concerns about shortages of goods could lead "to a significant increase in customers," in a statement emailed to CNN, and suggests stores should consider planning for extra security.
James Martin, Policy Advisor on Crime at the British Retail Consortium, said Friday that UK retailers are well-informed in security matters.
"Even if circumstances change, retailers are well-versed in providing effective security measures to protect customers and employees. The British Retail Consortium and our members will continue to work with police to do that," Martin said.
"Retailers across the country will continue to work with the police and other partners to keep retail sites running smoothly."
The news of possible stockpiling comes after Dave Lewis, the chief executive of supermarket chain Tesco, revealed the retailer was working with suppliers to stockpile non-perishable goods -- like tinned food -- in case the UK leaves the European Union on March 29 without a deal.
"The biggest challenge will be where it's hard to get that sort of contingency in places when it comes to fresh food, where you can't stockpile," Lewis said in a conference call with journalists on Thursday.
"Like all food retailers, we'd be very keen that there was no sort of friction at the border, given that the UK imports about half of the fresh food that it eats," he added.
A stroll around Marks & Spencer's grocery department shows how produce like oranges, raspberries, apples and salad leaves are imported to the UK from EU countries such as Italy, France, Spain and Portugal.
The UK has ramped up contingency plans in recent weeks as the chances of a no-deal Brexit rise.
The Department of Health told CNN Friday that it had signed two contracts "shortly before Christmas" to secure space in warehouses to store drugs as part of its no-deal planning.
In December, ministers agreed that an emergency contingency plan was essential in case parliamentarians reject Prime Minister Theresa May's deal when they vote this month.
No Brexit at all?
On Friday, Foreign Secretary Jeremy Hunt told the BBC's Radio 4 that there is a possibility that the UK might not leave the EU at all if May loses Tuesday's parliamentary vote on Brexit.
"Up to now people quite rightly have been worrying about the prospect of no deal, but now there's another possibility coming into sight, which is actually no Brexit. And why is that? We have a government that's committed to delivering Brexit, but it doesn't have a majority," Hunt said.
The Foreign Secretary added that if May's deal is rejected, there might not be opportunities for another type of Brexit.
"What we may end up with is not a different type of Brexit, but Brexit paralysis, and Brexit paralysis ultimately could lead to no Brexit," he added.
Hunt said that outcome could be "incredibly damaging" as it would breach the trust of people who voted for Brexit, and added it would also damage Britain's reputation abroad because of its inability to deliver on Brexit.