“That’s how you can get to a position to open society at least within your borders and then figure out how you’re going to do your border checks.
“Whether it’s testing at airports, screening passengers, bridges with other countries to have low numbers.
“But I think that needs to click in people’s head that this is actually a long term problem and the best way through it for the next few months is to actually get rid of the virus because living with it is going to be painful.”
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She added: “I think it will have to start on a country by country basis because there are some countries who have done it effectively like Vietnam, Thailand, New Zealand.
“But there are other countries like Brazil and India where no matter what they try, with their population size they will not be able to feasibly do this.
“I think within the UK, we are an island, we have a major advantage. Our cases have come down.
“There has been remarkable compliance and I think the message is, people have sacrificed for weeks. Don’t let that sacrifice go to waste by the numbers jumping up again.”
Her comments come as Boris Johnson will discuss reopening the hospitality sector and loosening the two-metre social-distancing rule in England with his top Cabinet colleagues and scientists.
The Prime Minister and his most senior ministers will on Monday discuss the next steps for the lockdown with chief scientific adviser Sir Patrick Vallance and chief medical officer for England Professor Chris Whitty.
Mr Johnson will then on Tuesday outline the plans to Parliament for pubs, restaurants, hotels and hairdressers to reopen in England from July 4, and a likely loosening of the distance rule to aid the restart to the economy.
On Sunday, the PM said the progress made in the fight against coronavirus during three months of lockdown mean “it will be possible to open up more”.
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He added: “The disease is increasingly under control and I just want people to reflect on that important fact.”
Guidance will be published for each sector on how businesses can reduce the spread of Covid-19 when they reopen.
And the public are expected to be warned that the newest relaxation of rules will be the first to be reversed if there are widespread breaches that prompt the virus to spread uncontrollably.
A No 10 spokesman said: “The reason we are able to move forward this week is because the vast majority of people have taken steps to contain the virus.
“The more we open up, the more important it is that everyone follows the social-distancing rules. We will not hesitate to put the handbrake on to stop the virus running out of control.”