Boris Johnson has promised to take tougher action at Britain's borders to protect the country from new Covid variants.
The Prime Minister refused to be drawn on when the current lockdown could be lifted, although he said the Government wanted to 'do everything we can' to reopen the country.
However, he added the country must be cautious about relaxing measures to avoid another coronavirus wave, which could plunge the UK into a fresh shutdown.
Mr Johnson came under fire this week after it emerged he ignored the Home Secretary's advice to shut down Britain's borders in March.
Speaking today about tougher border controls, he told reporters: "I really don't rule it out, we may need to take further measures still.
"We may need to go further to protect our borders.
"We don't want to put that [all the effort to control the virus] at risk by having a new variant come back in."
Earlier this week, a recording was leaked in which Priti Patel told Tory supporters that she wanted Britain's borders to shut at the start of the pandemic.
In the video call, she said: “On ‘should we have closed our borders earlier’ the answer is yes, I was an advocate of closing them last March.”
She was understood to have been concerned that flights from coronavirus hotspots including Tehran, New York, Rome and Beijing were still being allowed to land.
After the leak, Mrs Patel claimed that in March “no one could speculate or even conceive” how deadly coronavirus would be.
Mr Johnson claimed at PMQs that the UK had “one of the toughest border regimes in the world” - even though it only shut travel corridors last weekend.
Speaking at the Downing Street press conference today, the Prime Minister warned that any relaxation of restrictions will have to be carefully considered.
He added: "I think we will have to live with coronavirus in one way or another for a long while to come. I think it is an open question as to when and in what way we can start to relax any of the measures.
"Obviously, we want to do everything we can to open up but only safely, only cautiously.
"I also think that the British public and British business would much rather we opened safely and cautiously when it was right to do so rather than opening up again and then being forced to close back down simply because the virus takes off again.
"I think that is a far more sensible approach.
"The first thing that we want to be able to reopen if we can make any progress will, of course, be schools."
England's Chief Medical Officer Professor Chris Whitty said the coronavirus situation in the UK remained "extremely precarious".
He said: "In terms of the infection rate, if you took the country as a whole and just averaged it, then the number of infections is broadly going down but it is at a very high level, and it is extremely precarious - I really want to stress this.
"A very small change and it could start taking off again from an extremely high base, and there are some areas of the country and some age groups in which it does not appear to be going down - for example in people (aged) 20-30, the evidence is that it may still be increasing in some parts of the country.
"It is not solidly going down and it is very, very high."
Prof Whitty said the peak of deaths "may well be still in the future", before warning: "If people took this moment and said, 'Right, it is over', it would get back into very deep trouble very fast and the NHS is absolutely at the top of what it can manage.
"If that happened again, we would be in really, really deep trouble."