Tony Blair has suggested there will be a point where a "very large" proportion of the whole UK population will need to be tested for coronavirus to track the disease.
It comes as Cabinet Office minister Michael Gove said 10,000 people a day are now being tested and the government aims to increase that figure to 25,000 a day.
Mr Gove has refused to give a timeline for when all NHS and social care workers will be tested, despite increasing demands.
Instead, he said it is hoped to "be able to test as many frontline workers at the earliest possible stage".
Raising the possibility of mass testing in the UK, former prime minister Mr Blair told Sky News' Sophy Ridge on Sunday there was a risk of the disease resurging when the country's restrictions begin to be eased, so health authorities would need to be able to deal with this.
He said: "Your risk, obviously, is as you start to ease the lockdown, how do you then deal with any resurgence of the disease? This, of course, is what they're now dealing with in China and South Korea, and elsewhere.
"Unless you have that testing capability that you can apply at scale, and by the way when I say mass testing I mean I actually think you will need to get to the point where you've got the capability, and I assume we're preparing for this now, of testing literally a very large proportion of the entire population.
"You may have to do those tests two or three different times because you need all the time to be able to track what's happening with the disease, to learn where, for example, there may be a surge or a hotspot of it, and take immediate action."
When asked what percentage of the population may have to be tested, Mr Blair replied: "I think you're talking about virtually everybody."
Health Secretary Matt Hancock, who is in isolation after testing positive for COVID-19, tweeted the government had reached 10,000 tests a day ahead of schedule, and were "on track to 25,000".
GP Richard van Mellaerts said more widespread testing was needed.
He said: "I think that we need to have far wider testing than we have at the moment. When we look at those counties around the world like South Korea that have been doing vast amounts of testing.
"They've got a much better grasp of what's going on. If we can start crunching the data - find out where the hotspots are, who's at risk who's not, who can go back out into the workforce and who can't, then we'll have a far better hold over this.
"And it's so crucial with healthcare workers that we know who's infected, who's not, who's immune, who's not. So that we can get as many people back out into the workforce as quickly as possible."
Meanwhile, the chief executive of the Royal College of Nursing has said about 20% of frontline workers have had to take time off work to self-isolate having shown symptoms of coronavirus.
Dame Donna Kinnair told Sophy Ridge that nurses would like to be tested so that they are able to get on with their jobs.
Asked about the proportion of nurses or NHS workers who have had to take time off, Dame Kinnair said: "Last week it was about 20% of nurses, or frontline workers, who were doing it.
"I don't know the exact proportion of nurses in that, 20% to 25%, so there are a number of nurses who would like to be tested to get on with their job if they are not positive for COVID-19."
The search for a vaccine is continuing and there are at least eight "in the pipeline", according to former chief scientific adviser Sir Mark Walport.
He told Sophy Ridge: "There is enormous international scientific co-working on this. CEPI (the Coalition for Epidemic Preparedness Innovations), which the UK has just committed Â£210m to, has been working across the world on vaccine development.
"They have eight in their active pipeline at the moment, one of which is one that UK Research and Innovation and others have been funding in Oxford. And so there is an enormous amount going on and... science and technology and innovation is critical to both providing the advice and the management.
"The reality is that we need to be sure that a vaccine is effective and doesn't have side effects and so it will take probably a year to 18 months."
He added: "The scale-up of that particular Oxford vaccine - whether it stands a better chance than any of the others, who knows. We'll be able to manufacture up to a million doses fairly quickly but of course that's a long way from protecting the whole population."