The government will not draw up a list of critical jobs that will be exempt from full self-isolation if workers are “pinged”.

Instead, employers will have to apply to government departments to allow workers to effectively circumvent the rules.

Boris Johnson announced on Monday that critical workers, who have been fully vaccinated for at least two weeks, will be able to leave their isolation to travel to work and do their jobs but must remain at home in isolation otherwise.

“But for the vast majority of us, myself included, I’m afraid we do need to stick with this system for now,” he said on Monday from his Chequers retreat where he is self-isolating.

A list of specific jobs was expected but instead, the prime minister’s spokesman said the exemption would be determined case by case, with employers having to apply to the relevant government department to see if their workers can continue to come into work after they are identified as close contacts of someone who has tested positive for COVID.

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The spokesman said it could include certain workers in the food industry, utilities, border staff and the NHS, but there is no blanket exemption for sectors.

He added: “I don’t have a specific number for you at the moment. As these discussions proceed we might have a clearer sense of the numbers, but as the prime minister set out yesterday it will be a very low number of people.”

Asked if it will be on the scale of hundreds or thousands, the spokesman said: “I wouldn’t want to set specific numbers on it at this point.”

On whether supermarket workers specifically would be included in the exemption, he said the government is “not seeking to draw lines specifically around who or who is not exempt” but it is important to “make sure critical services are able to function”.

Vaccines minister Nadhim Zahawi earlier said the exemption would cover those in “circumstances where there would be a serious risk of harm to public welfare if people in critical roles are unable to go to their workplace”.

A government spokesman added on Monday evening it is “not a blanket exemption for any sector or role” and employers will receive a letter from the relevant government department informing them and telling them what steps to follow.

But the advice appears to have changed slightly, with the onus on employers to contact the government instead of the other way around.

The prime minister had come under increasing pressure to change isolation rules for close contacts of positive cases who are working in essential industries as it was crippling businesses.

Dubbed the “pingdemic”, a growing number of people have been alerted by the NHS COVID app in recent weeks, meaning lots of critical workers without symptoms – who cannot work from home – are having to self-isolate.

In the first week of July, more than half a million people were told to self-isolate, a 46% increase on the previous week and a number that is continuing to rise.

The government said it does not plan to reduce the sensitivity of the app to avoid people being pinged as a third of those told to isolate develop symptoms.

Mr Johnson and Chancellor Rishi Sunak were also heavily criticised for saying they would be taking part in a pilot where they take daily tests instead of self-isolating after coming into contact with Health Secretary Sajid Javid, who tested positive.

They quickly performed a U-turn and said they would self-isolate, with Mr Johnson insisting he was not above the rules.