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”.

Secretary of state for business 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.

He was also forced to tell businesses to continue following the isolation advice after a boss of a food distributor revealed he was asking delivery drivers to take tests and not quarantine.

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.

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”.

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.