The chancellor, Rishi Sunak, is expected to announce that the taxpayer will pay self-employed workers up to 80% of their recent earnings to help contain the economic impact of coronavirus, as 470,000 extra benefits claims sparked warnings of an “unemployment crisis”.

Sunak has been under growing pressure to do more for the UK’s 5 million self-employed after announcing an unprecedented job retention scheme for employees last Friday, that will see thousands paid to stay at home.

It comes as Covid-19 claimed the life of a 21-year-old woman from Buckinghamshire, according to her family, and Britain’s deputy ambassador to Hungary, who was 37. The number of confirmed UK cases stood at just over 8,000 on Wednesday night.

The prime minister promised on Wednesday that the government was preparing to “put its arms around every worker.” He said the self-employed would be offered “parity” with employees – though Whitehall sources cautioned that did not mean the two schemes would be identical.

Details of the support package were still being finalised last night, but sources with knowledge of the plan suggested it would echo the promise of covering 80% of recent earnings that Sunak made to employees last week.

It could be subject to a lower cap than the £2,500 in monthly pre-tax income available in that scheme, however – because the self-employed tend to pay less tax. Some groups, including those already claiming universal credit, could be excluded.

Speaking at the daily Downing Street press conference, the prime minister said: “I genuinely don’t think there’s been a time in our history in the last century, certainly, when the government of this country has put its arms around so many people to get us through a very tough time. We will get through it, and we will get through it together.”

Sunak significantly increased the generosity of universal credit as part of last week’s package, and made it available to more self-employed workers.

A sharp surge in claims for universal credit has underlined the severe economic toll the coronavirus is already taking on Britain’s workforce.

The work and pensions secretary, Thérèse Coffey, revealed on Wednesday that 477,000 people had applied for the benefit in the past nine days. That is more than during any entire month of the 2008-09 financial crisis.

“We don’t know if they’re self-employed or at different stages, and I want to assure people that help, even if it’s not currently the level of help they would like, is there to help them through the safety net of the welfare state,” she said.

Karl Handscomb, senior economist at the Resolution Foundation, said: “The unprecedented surge in new universal credit claims shows that the UK is already in the midst of an unemployment crisis. The increase in claims is putting huge pressure on our social security system, and is driven by a huge hit to family incomes.

“The government was right to increase the generosity of the benefits system last week. It now needs to ensure the resources are there so that claims are processed quickly, and people receive support as soon as possible.”

The Department for Work and Pensions (DWP) is redeploying 10,000 staff to help process the extraordinary upsurge in new applications, making it the department’s main focus in the weeks ahead.

Its permanent secretary, Peter Schofield, said: “We made a decision that managing claims and making payments is a number one priority for DWP. Operationally we can deprioritise other things.”

The department has so far redeployed 1,500 members of staff to help with the sharp rise in universal credit claims, and is to increase this to 3,900 by the end of the week.

The shadow chancellor, John McDonnell, who will return to the backbenches in ten days’ time when a new Labour leader takes over, used what is likely to be one of his final speeches from the frontbench to call for the government to announce details of its scheme for supporting self-employed workers urgently.

“If people claim fraudulently while still working, they will rightly be prosecuted. But right now millions of cabbies, childminders, plumbers, electricians, painters and decorators and actors have all lost work or closed down their businesses. As have builders, designated as the self-employed under the construction industry scheme and they have no income. They need a solution, now,” he said.

Meanwhile businesses continued to demand clarity about who can keep travelling to work, as firms called for workers to come in despite Monday’s plea by the prime minister for the nation to “stay at home”.

Carolyn Fairbairn, director general of the CBI, tweeted: “It’s clear that many firms do not know whether to stay open or to close.” She said she would meet the business secretary and request better guidance.

The warnings come amid widespread confusion among businesses about how to respond to the lockdown. Halfords, the car parts, bike and servicing group, is reopening some of its stores this week after being designated an essential service. It had closed its shops on Monday night as Johnson addressed the nation.

Mike Ashley’s Sports Direct retail chain had intended to remain open but was forced to backtrack after a public outcry.

Frances O’Grady, the director general of the TUC, said the government needed to crack down on non-essential companies making staff attend work, telling ministers they needed to directly intervene if employers flouted the rules.

“Companies like Sports Direct shouldn’t be putting their profits before people’s lives. No one in non-essential services should be forced to go to work. And no one should be sacked for following official instructions and staying home,” she said.

Off-licences and other shops licensed to sell alcohol are now allowed to stay open, after an 11th-hour change, while several companies are lobbying ministers to be allowed special treatment.

The mayor of Greater Manchester, Andy Burnham, called for tough enforcement action against companies forcing their staff to travel to work in non-essential jobs during the lockdown.

“This is wrong. It’s risking the health of workers, their families and wider society. In the absence of a clear government instruction to end non-essential work I am taking legal advice about whether Greater Manchester police or other agencies can take enforcement action against companies which are exposing their employees in this way.”