He urged Boris Johnson put measures in place to contain and control the virus to prevent another outbreak of cases in the fall.
The former prime minister also accused the government of inconsistent messaging on face masks, which became mandatory in stores in England on Friday.
And he claimed that, as another lockdown in the UK was unrealistic, the masks would help control coronavirus, as in many other countries.
Mr. Blair recorded an interview for Sophy Ridge on Sunday as he launches a new report on wrestling coronavirus by its think tank Institute for Global Change.
In its report, the institute calls for the widespread wearing of face masks and social distancing for some time to avoid a second wave of coronavirus cases as lockdown rules are relaxed.
The former prime minister began his interview by criticizing the government’s record on testing.
« We are doing infinitely better than we were, we are testing a lot more people, ”he admitted.
“But I still don’t think we have the right strategy in place for what I would call mass testing, and if you think our capacity is 300,000 tests per day, we’re probably not using, of after our calculations, that about half of that.
“We will soon have a capacity of 500,000 tests per day. We should be using all of this and that means dramatically increasing the number of people who have access to testing and using data and local communities much more effectively to do so.
“And the reason I still think we’re a long way from where we need to be is, if you analyze what we know about this disease now and look at the global data, the reality is we’re going to be living with COVID-19. , we are not going to eliminate it. ”
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Asked for how long, Mr Blair replied: “Well, for the foreseeable future, enough for the future, that means it’s worth putting the containment infrastructure in place that allows you to control it.
“Because the problem is if you look at it in the last few days you’ve had outbreaks in Poland, Australia, Romania, Israel, Argentina, several other countries.
“So there’s a pattern that’s developing, is that people get stuck, they make it easier to lock in, but then there are significant spikes.
“And we are still in the summer months when it is frankly easier to cope with the disease. You may end up with a resurgence in the fall. ”
He added, “Now that may not happen, but you have to hope for the best and plan for the worst. And so what we’re doing in the document we released from the institute is suggest a whole range of things that you could do now that would allow you to put that containment infrastructure in place. ”
Asked whether the government’s message on face masks had been clear and consistent, Mr Blair replied: ‘No, I think even the most ardent supporter of the government would say that.
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“They started by saying it wasn’t necessary. I think we said two or three months ago that it was obvious that we were going to go in the direction of the masks.
“There are some things that are just obvious when you look at them. And the evidence on masks, by the way, is absolutely clear to the world, there is no doubt that they help control the disease.
“If you look at the countries that have used masks a lot, not just the Asian countries where it is more part of normal culture, but take a country like Austria, where they have used masks a lot, there is no doubt. that they did better control the disease.
“And it’s all about controlling it, because if you think you can’t really get locked out… and I think it’s just unrealistic to think we’re going to be able to do that.” “