Supermarkets have warned that the growing number of traders forced to isolate themselves is starting to affect the availability of some products.
The cooperative said it was "missing some produce", while Iceland said stores may have to be closed.
Sainsbury 's said it "did not may not always have the exact products people wanted, but played down shortage fears by saying theproblem was not widespread.
Iceland also urged buyers not to panic to buy, saying it was not necessary.
The Secretary of Businesswoman Kwasi Kwarteng said the government was "concerned about the shortages".
"I don't want people to feel like every shelf in every supermarket is bare - it's not, but we are certainly concerned about shortages, we are looking at the supply chains of critical industries and we are looking at this situation, "he added.
A record 618,903 people in England and Wales have been " pinged by the NHS Covid app on weekdays through July 14.
Supermarkets and other industries, including hospitality and transportation, said a number An increasing number of employees have been affected, which means they have to isolate themselves for 10 days. Some companies have reducedhours of operation to deal with staff shortages or shut down parts of the business.
Companies want people who are double vaccinated or who have daily tests to be able to return to work.
'Isolated incidents '
Mr. Kwarteng said the government would later issue guidance on which sectors would be exempt, although he declined to say whether this would include the food industry.
Numerous Thursday newspapers published images of empty shelves at some supermarket branches - with some depicting panic buying of certain items - but industry sources said to Hfrance.fr that until now, food shortages were not a systemic problem.
Iceland's Managing Director Richard Walker said the photographs of empty shelves in supermarkets were "isolated incidents ".
Meanwhile, the co-op said it was hit " by some disruption uneven delivery and in-store operations ".
" We are working closely with our suppliers to restock quickly, "he added.
It is understood that items such as soft drinks, personal care products such as deodorant and beer are the most affected.
Lidl said the increase in the number of employees needing to self-isolate is starting to touch operations, but it was strivingto minimize disruption.
About 1,000 Icelandic employees - almost 4% of its ff staff - are currently absent forreasons related to Covid, the north of England being the most affected.
Of these, 27% tested positive for Covid, while 64% were "pinged " by the NHS Covid app and told to isolate.
Iceland is recruiting 2,000 temporary workers to deal with shortages while the cooperative will hire another 3,000 workers.
The British Retail Consortium (BRC) said the growing number of workers in demanded to isolate "was putting increasing pressure on the ability of retailers to maintain opening hours and stock shelves ".
A drop in the number of drivers of available heavy goods vehicles, exacerbated by the growing number of people forced to isolate, has also been "causing minor disruption of some supply chains ", said Andrew Opie of the BRC.
The Road Haulage Association estimates that there is a shortage of 100,000 truck drivers inUK due to workers returning to Europe after Brexit as well as delays in testing carriers for Covid.
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Meanwhile, the British Meat Processors Association has said that some members are seeing between 5% and 10% of their workforce "ping " through the app .
Under current self-isolation rules in England, anyone identified as a close contact of a confirmed positive case must be isolated for 10 days,whether or not he received both doses of a vaccine.
If someone is isolated by NHS Test and Trace, they are legally obligated to do so.
But if someone is "pinged " by the NHS Covid app, the requirement to self-isolate is advisory only.
Andrew Selley, managing director of Bidfood UK, which supplies products to hospitals, nursing homes and prisons as well as restaurants, said he was calling on workers who have been 'pinched' to resume work after passing a negative PCR test.
"We carry out lateral flow tests daily away from their workplace and if it is negative then they can continue with their work " Mr Selley said.
But Mr Kwarteng told Hfrance.fr: "The rules are clear and I think they must be followed.
Earlier this week, the government announced that A "small number " of fully immunized critical workers, including health and care workers, would be allowed to continue doing their jobs even if they were in close contact with someone who had tested positive for Covid.
The prime minister said he did not want to extend the exemption too widely in order to limit the spread of the virus.
The government argued that it was necessary to keep the isolation rules largely unchanged until August 16.
From that date, fully vaccinated people and those under the age of 18 will be able to avoid self-isolating by doing daily Covid tests.
Dozens of tips across England were also forced to suspend bin collection due to staff self-isolation .
On Wednesday BP said there was a shortage of truck drivers and staff isolation had caused fuel supply problems at some of its gas stations .
The oil company said shortages of unleaded petrol and diesel have seen a "h andful " as its UK sites are temporarily shutting down.
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