Boris Johnson has said that he knew the public was "furious with me and the Government" over the lockdown measures and warned that the country was set for a "bumpy" approach to Christmas.
In an interview with the BBC, Mr Johnson said: "I appreciate the fatigue that people are experiencing... but we have to work together, follow the guidance and get the virus down whilst keeping the economy moving."
He said : "They're furious at me and they're furious for the Government, but... I've got to tell you in all candour it's going to continue to be bumpy through to Christmas, it may even be bumpy beyond.
"But this is the only way to do it."
Mr Johnson said the country needed to face the fact that it could be "a very tough winter".
However he insisted that Britons should behave "fearlessly" but with "common sense", as he set out the need to balance controlling coronavirus and protecting the economy.
"On the one hand we have the imperative to save life, it is a moral imperative to save life if we possibly can," Mr Johnson said.
"On the other hand we have to keep our economy moving and our society going."
"That is the balance that we are trying to strike and that's why we have got the package of measures now that are in force both nationally and locally.
"What we want people to do is behave fearlessly but with common sense, to follow the guidance - whether national or local - get the virus down but allow us as a country to continue with our priorities."
The PM said he hoped the "scientific equation will change" would change in the coming months, with the prospect of mass testing and a vaccine.
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And he hit back at criticism of his handing of the coronavirus crisis from restive Tory backbenchers.
He said: "I think the reality is this is a Government that is facing an unprecedented crisis and I think if people wanted me to approach it with the sort of buoyancy and elan and the qualities I usually bring to things, I think people would think that was totally inappropriate."
He said "we face a pandemic that in which already tens of thousands of people have died", adding that: "The struggle we have now is to contain that pandemic and yet to keep our economy moving.
"And what I can certainly tell you is that as soon as we have done what is necessary and we have got the virus under control... then you will see this country and this Government and this country really accelerating our progress."
