A “very narrow” list of sectors whose workers will be exempt from isolation rules will be published on Thursday, the Business Secretary has said as the Government struggles to contain the “pingdemic”.

Kwasi Kwarteng told shoppers not to panic over supermarket shortages as retailers warned the situation around alerts from the NHS app is “untenable” and requires an urgent rule change.

As a record was set when the number of pings exceeded 600,000 in a week, he told businesses to follow the isolation advice after a boss of a food distributor revealed he was asking delivery drivers to take tests over quarantining.

Downing Street this week suggested that there would be no list of sectors whose fully-vaccinated workers could face loosened isolation restrictions to prevent staff shortages.

I think what the most important thing for Government to do is to recognise that the current situation is untenable

But in the face of mounting pressure, Mr Kwarteng said: “We’re looking at different sectors and we will be publishing today the sectors that will be affected.”

He told BBC Radio 4’s Today programme that “I don’t think it’s a question of applying for this”, despite No 10 having said businesses need to apply to Government departments.

Mr Kwarteng said he would not “pre-empt” the list when asked if the food industry would be on it, amid pleas from bosses to prevent major staff shortages as Covid-19 cases soar.

But he told BBC Breakfast the list would be “very narrow, simply because we don’t want to get into a huge debate about who is exempt”.

NHS figures showed a record 618,903 alerts were sent to users of the NHS Covid-19 app in England and Wales in the week to July 14, telling them they had been in close contact with someone who had tested positive for coronavirus.

Iceland’s managing director, Richard Walker, said the supermarket was having to hire 2,000 temporary workers to prepare for “the exponential rise in pinging”.

Mr Walker told Today: “The dramatic pictures that you might have seen in the media are isolated incidents and not widespread.

“But the people who should be panicking are the Government, and I believe that, you know, the sooner they clear up this mess, and get retail workers and HGV drivers on to the key worker list, the better.”

Mr Kwarteng responded: “He was right to say shoppers shouldn’t be panicking.

“I don’t quite know what he meant that the Government should be panicking, I’m not panicking.”

The British Retail Consortium (BRC) has urged ministers to “act fast” to allow fully-vaccinated workers, or those who test negative, to be exempt from isolation after a “ping”.

The Government will introduce a wider relaxation for all double-jabbed individuals but that will not come until August 16 – a month after most coronavirus laws ended.

That date “feels a long time away”, however, BRC chief executive Helen Dickinson said, as she warned stores are closing, hours are being reduced and consumers are facing reduced choice.

“I think what the most important thing for Government to do is to recognise that the current situation is untenable,” she told BBC Breakfast.

Boris Johnson announced the plan for a “small number” of critical workers to be able to continue their roles despite being pinged as he scrapped most of England’s Covid restrictions on Monday.

On Tuesday, the Prime Minister’s official spokesman said: “It’s not a blanket exemption and my understanding is we’re not going to be producing a list covering individual sectors, these business-critical areas will be able to apply for exemptions to their host departments.”

But the Government appears to have changed course on that amid mounting criticism.

A lorry driver shortage was putting increased pressure on the country’s grocery supply chain and empty shelves were witnessed in some supermarkets across the country.

Mr Kwarteng had to tell businesses to “stick to the rules” after a food distribution company struggling with staff shortages advised workers who are pinged by the NHS app to take tests and continue working, in breach of the Government advice.

Bidfood chief executive Andrew Selley defended his approach for delivery drivers to continue working if they have negative results as “appropriate and safe” for the “critical workers”.

“If they are pinged we ask them to take a PCR test, if that’s positive then clearly they’ll isolate but if it’s negative we ask them to come back to work and we have a process of doing lateral flow tests daily away from their workplace and if that’s negative they can proceed with their work,” he told Today.

But Mr Kwarteng responded: “I would stick to the rules, which are very clear, which say that if you are pinged you should self-isolate.”

Professor Ravi Gupta, a scientist advising the Government as part of the New and Emerging Respiratory Virus Threats Advisory Group (Nervtag), described it as a “mixed bag of measures which are creating confusion and havoc”.

“I think it is a little bit difficult to justify people doing self-isolation when in fact we have held huge sporting events with large amounts of transmission that have probably gone undetected,” he told Sky News.

“So it’s a sort of half-hearted measure that is affecting the lives of many people, many of whom will be depending on their income on a daily basis, and for whom a week of isolation is disastrous.”

Dr Tom Dolphin, a spokesman for the British Medical Association and a consultant anaesthetist in central London, said it was “very unfortunate” that people are deleting the app.

“I think that if you blame the app for it, it overlooks the point which is that the app is reflecting the huge rate of transmission in the community,” he told Sky.

“The reason there’s a pingdemic is because there’s a pandemic. People are being infected and testing positive in huge numbers, and blaming the app for that is like blaming the fire alarm for going off when there’s a fire.”

TUC general secretary Frances O’Grady said: “If we want to stop Covid spreading like wildfire through workplaces and wider society, the Government must support people to self-isolate.

“With hundreds of thousands of cases reported in the past week – and over half a million people pinged – it beggars belief that ministers are still refusing to provide decent sick pay.

“The baffling decision this week to exclude millions of low-paid workers from access to any form of sick pay looks more foolish by the day.

“We know that many working in hospitality and other frontline roles do not earn enough to even qualify for the statutory minimum. They shouldn’t be forced to choose between doing the right thing and being plunged into financial hardship.

“Staff shortages will continue to get worse unless the Government fixes our broken sick pay system.”

According to TUC analysis, two million workers in the UK do not earn enough to qualify for statutory sick pay.