More than 140,000 companies employing a total of about a million workers have applied to the government’s job furlough scheme on its first day of operation, the chancellor has announced.

It is understood the price tag attached to the requests is about £1bn, a figure that is likely to rise significantly as more companies make their applications for help over the coming days and weeks.

Rishi Sunak said the government had delivered on its promise to pay wages for threatened jobs, under a programme that allows employers to lay off staff temporarily and claim up to 80% of their salaries from the state, up to a maximum of £2,500 a month.

Speaking at the daily Downing Street press conference, he said: “Exactly a month ago today I stood at this lectern and said we would help to pay people’s wages. We promised support would be available by the end of April. Today, we deliver our promise.”

Expressing hope that the economy could still quickly recover from the coronavirus outbreak, Sunak said the first million people being furloughed were at risk of losing their jobs without the government’s support.

The chancellor said getting the coronavirus job retention scheme system (CJRS) up and running was a “remarkable story of public service” as thousands of HMRC staff had either worked overtime or come out of retirement to help. The system is able to process up to 450,000 applications an hour, while it will take companies up to six days to receive funds.

HMRC has deployed 9,500 staff to deal with queries. Fears that the website could crash and that phone lines would be overwhelmed looked to be unfounded, as business groups said the scheme had got off to a smooth start. However, business leaders warned there was no room for error, as many employers would need to run their payrolls this week.

The government has also been criticised over the rollout of its coronavirus business interruption loan scheme (CBILS), which is designed to help small and medium-sized businesses. Sunak said on Monday that the number of loans offered under the scheme had risen to 12,000 from 6,000 last week.

A spokesman for the business lobby group the Institute of Directors said: “Another acid test will be the money reaching firms’ accounts.”

Against the backdrop of a potentially prolonged government lockdown, after ministers opted to keep tough restrictions on social and business activity in place for at least another three weeks, the job retention scheme has been extended until the end of June.

As many as 8 million workers could be furloughed in total, according to estimates from the Resolution Foundation thinktank, which warned low-paid hospitality and retail companies would be affected most. It said the cost of the scheme after the first day alone would be £4.2bn over three months, although that figure is expected to rise sharply.

The Office for Budget Responsibility, the government’s independent economic forecaster, had put the cost of the scheme at £42bn before the extension was announced. Employers can only claim for furloughed employees who were on their payroll on or before 19 March, and there are fears that many people will fall through the cracks. The scheme does not cover everyone who recently switched firms, or seasonal workers who were about to start jobs at holiday parks, airports and youth hostels.

The culture secretary, Oliver Dowden, said earlier on Monday that firms should only use the scheme if they could not afford to pay staff themselves.

Asked on ITV’s Good Morning Britain about reports that Victoria Beckham was using the scheme for staff at her fashion company, Dowden would not comment directly, but added: “The clear principle is: you should only be using it [the scheme] if you have to.”

He had previously warned Premier League football clubs that the scheme was for struggling firms and was not intended for “billionaire owners”.

Workers locked out of the scheme continued to call on the chancellor to extend its coverage. The entertainment industry union Bectu said a last-minute change on Friday meant that employees in TV and film who were on fixed-term contracts that ended before 19 March were no longer able to go back to their last employer and ask them to extend their contract and furlough them.