More than 110,000 self-employed people whose businesses are affected by coronavirus have already applied for government grants on the first day of the scheme's operation.
The value of the claims made so far is more than £340m, said officials.
The Self Employed Income Support Scheme is designed to match the support being given to furloughed employees.
The grants will be calculated as 80% of average monthly profit over a period of up to three years.
The government said the money would be paid into the accounts of eligible people six days after applying.
The maximum payment will be £7,500, intended to cover March, April and May.
The scheme is the biggest direct financial support package for freelancers and the self-employed since lockdown started.
The process is being run by HM Revenue & Customs (HMRC), which has been operating and overseeing loan schemes and the government's furlough payments.
HMRC says most of the 3.5 million people affected should have been contacted, and invited to get ready to make a claim by using its eligibility checker.
They will then have been given a time at which to apply, between Wednesday and 18 May, although if applicants are unable to file at that time HMRC says they can still go ahead and apply.
Inevitably, some people's records will not be up to date or they may not be at their normal address. HMRC says anyone who thinks they are eligible but has not heard from it should go to its website and use the checker tool. Claims can then be made from 17 May.
Most should receive any money they are entitled to from 25 May.
The scheme was unveiled in March after the government faced criticism for failing to provide support for self-employed and freelance workers in its earlier package of economic measures.
Derek Cribb, chief executive of the Association of Independent Professionals and the Self-Employed, said the scheme extended "a much-needed lifeline to those self-employed people who are eligible for it".
"For the self-employed, coronavirus is not only a health crisis, but also a pressing income crisis, until now they've been coping either by applying for Universal Credit or by digging into their savings."
However, those who started in business from early April last year will miss out, as will those who pay themselves just with dividends from a limited company. Mr Cribb urged the government to extend the scheme to include those groups too.
The government has not said whether the initiative will be extended into the autumn in line with the furlough scheme, which protects 80% of employees' wages up to £2,500 a month.
On Tuesday, Chancellor Rishi Sunak announced that scheme was being extended until the end of October.
Mr Sunak said: "With payments arriving before the end of this month, the self-employed across the UK will have money in their pockets to help them through these challenging times."