Boris Johnson told his daily coronavirus Covid-19 briefing he had hoped 250,000 people would answer the Health Secretary Matt Hancock's call last night - with that target smashing in just hours.
He said: "I can tell you that, in just 24 hours, 405,000 people have responded to the call. That is already, in one day, as many volunteers as the population of Coventry."
They will be driving medicines to patients' homes, bringing patients home from hospitals, and "making regular phone calls to check on and support people staying on their own in their home", Mr Johnson said.
He again said described the NHS as a "world class" health service, but said, like any other, it has a limited number of medics and equipment, and said his home arrest restrictions put in place earlier this week was to help it manage.
"The more people that get sick, the harder it is to cope," he said. "So it's vital to delay the spread of the disease and reduce the number of people needing treatment at once.
"I want to remind everyone of our core policy: Stay at home, protect the NHS, and save lives."
Meanwhile, sweeping emergency powers to tackle the crisis are set to become law after the Coronavirus Bill cleared the House of Lords without amendment and was granted royal assent.
The public will be able to conduct antibody tests at home in a matter of days, MPs were also told, though that claim was later thrown into doubt.
Some 3.5 million kits have been bought but will be tested for their effectiveness before being made available to buy on Amazon and in pharmacies.
NHS and key workers will be given priority, meaning they are safe to go back to work if they have had the virus already - and should, it is hoped, be immune.
Prof Sharon Peacock from Public Health England's National Infection Service, said: "Once we are assured they do work, they will be rolled out into the community."
The UK's chief medical officer Prof Chris Whitty said there was a "global bottle neck" on buying more testing kits, and said: "Every country wants this new test for a disease that wasn't being tested for anywhere three months ago.
"Everybody wants it, so there is a global shortage. The next priority is to get critical workers back to work or to say to them, 'You have got it'. We definitely would like that."
The latest figures on confirmed cases and deaths in the UK had not been released by 5.30pm.
There were eight confirmed cases in Blackpool by 9am yesterday, plus 71 in Lancashire, though tests are only being done in hospital so the figure is feared to be much higher.
Mr Johnson said a tailored package of support will be announced tomorrow to help the self-employed, and said the country is coping "very well" with the crisis.