Mr Sunak revealed employers will be able to begin bringing back staff on a part-time basis from July, a month earlier than previously announced, as the lockdown is eased across the UK.
And self-employed workers whose incomes have been hit by the coronavirus lockdown will be able to claim up to £6,570 extra support, the Chancellor said.
Having already confirmed the Coronavirus Jobs Retention Scheme, which has seen the government cover 80% of the wages for 8.4 million staff put on furlough, would be extended into October.
However, Mr Sunak had signalled that employers were likely to be asked to pay a share of the huge cost of the scheme, which it is estimated will add £15bn to public spending.
Industries that are set to be worst hit by the crisis and are likely to be asked to wait the longest to reopen, such as the hospitality and tourism sector, had asked for a further extension, flexible extension.
From August, businesses will need to cover employer national insurance and pension contributions on behalf of furloughed staff.
In September, they will also be asked to pay 10% of the salary guarantee, which is capped at 80% of earnings up to a maximum of £2,500 per month.
And from October, the employer’s share of salary costs for furloughed staff will rise to 20%.
Mr Sunak said: “Our top priority has always been to support people, protect jobs and businesses through this crisis. The furlough and self-employment schemes have been a lifeline for millions of people and businesses.
“We stood behind Britain’s businesses and workers as we came into this crisis and we stand behind them as we come through the other side.
“Now, as we begin to re-open our country and kickstart our economy, these schemes will adjust to ensure those who are able to work can do so, while remaining amongst the most generous in the world.”
Employers seeking to bring furloughed staff back part-time will need to demonstrate how many hours their employee will have normally worked to make a claim for part of their wages.
Part-time furloughed staff who believe they are not receiving the correct share of their wages from the government, based on their hours they are being asked to work, will be able to report their employers to an HMRC fraud line.
For the self-employed, workers whose 2018-19 tax return showed they earned at least 50% of their income from self-employment have been eligible to apply for a taxable grant of up to 80% of their average monthly profits over three months, up to £7,500. The scheme has just opened and applications can be made up to 13 July.
A second grant scheme will open in August on the same basis and cover 70% of average profits, up to £6,570.
Applicants must show that coronavirus has hit their income, but do not need to have applied for the first grant to be eligible for the second.