PM Boris Johnson says he is “hoping to avoid” another national lockdown in England but admits Covid cases have increased “very much” in recent weeks.
It comes after a tough new six-week lockdown was announced in Northern Ireland from 26 December.
Wales will also begin a lockdown on 28 December, while the Scottish government has said “nothing” can be ruled out ahead of a review on Tuesday.
Health bosses have warned that the NHS is already under significant pressure.
The president of the Royal College of Emergency Medicine, Dr Katherine Henderson, said England and Scotland needed to do “whatever it takes” to get a grip of the virus, even if that meant “full lockdown”.
Meanwhile, the R number – which represents how many people each infected person passes the virus onto – has risen above 1 in the UK.
The latest figure, calculated by the government’s scientific advisers, is estimated to be between 1.1 and 1.2, up from between 0.9 and 1 last week.
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Official figures show Covid-19 cases have risen in the last week in England, driven by sharp increases in London, as well as rises in the South East and East Midlands.
Asked whether England would end up following Northern Ireland and Wales into a national lockdown, Mr Johnson said: “Obviously we are hoping very much that we’ll be able to avoid anything like that but the reality is that the rates of infection have increased in the last few weeks.”
He said the Christmas rules, which are being relaxed across the UK between 23 and 27 December, were “very much a maximum” and “not a target people should aim for”.
The prime minister encouraged people to “think about our elderly relatives” to “avoid spreading the disease” over Christmas.
He added that he hoped next year, with the rollout of the vaccine, would “be very different indeed”.
Earlier, he tweeted a message warning people planning to form “Christmas bubbles” in the UK to start minimising contact with people from outside their households from today.
Labour leader Sir Keir Starmer said “nobody wants a third lockdown” but England’s tiered system was “not strong enough”.
He called for the prime minister to “toughen up over Christmas”, saying the Welsh government’s decision to limit Christmas bubbles to two households, instead of three, was a “step in the right direction”.
Former government adviser Prof Neil Ferguson, an epidemiologist from Imperial College London, said he was “more concerned” about what the country was going to be facing in early January than over the Christmas period itself.
He told BBC Radio 4’s World at One programme that very rapid increases in case numbers had left “very little headroom”, adding that any future lockdown in England may have to be tougher than the one seen in November.
Meanwhile, teaching unions have criticised the government’s announcement that the return to secondary school in January will be staggered to allow schools to set up a Covid testing scheme.
They say the move came too late for them to make the necessary preparations for testing but Mr Gibb, the schools minister, has defended the plan, saying the government would provide support.
Northern Ireland’s new six-week lockdown is essentially a return to March’s sustained restrictions, Health Minister Robin Swann has said, with non-essential shops and close-contact services such as hair salons having to close. Pubs, cafes and restaurants will be restricted to takeaway services.
The first week of the restrictions, running until 2 January, will see even tighter measures with essential shops, including supermarkets, having to close each day by 20:00 GMT.
No sporting events will be permitted at all – even at elite level – with people being urged only to leave their home for essential reasons.
In Wales, non-essential shops will close from the end of trading on Christmas Eve, with an alert level four lockdown starting four days later.
In England, some 38 million people will be subject to the nation’s strictest measures – tier three – from Saturday.
Scotland’s Health Secretary Jeane Freeman said the option for a post-Christmas lockdown in Scotland “remains on the table”.
The decision by all four UK nations to relax restrictions and allow more mixing for five days over Christmas has prompted concern that it will fuel a further surge in case numbers, with medical professionals warning the NHS is already under significant pressure.
Average NHS bed occupancy in England has reached almost 89% for the week ending 13 December, with 59 out of 126 NHS trusts reporting bed occupancy of higher than 90% – which is above the recommended safe level.
Dr Katherine Henderson told BBC News the UK was at a “really dangerous point where we could tip into finding it incredibly difficult to manage” and her colleagues were “increasingly” seeing ambulances queuing outside hospitals.
In Northern Ireland, Dr Martin Kelly, a consultant respiratory physician in Londonderry, told BBC Radio 4’s Today programme: “Right in the mouth of Christmas we’re seeing a significant further surge in numbers which is already putting the service under significant pressure.”
And Dr Nick Lyons, a health board medical director in south Wales, said things were similar in his region, where non-urgent procedures have been cancelled. The intensive care units “were basically full with Covid patients” while the area’s field hospital was “roughly at half its total capacity”, he told Today.
The UK recorded a further 35,383 cases on Thursday, along with 532 deaths within 28 days of a positive test.
However, this included 11,000 positive cases from Wales that were not previously recorded in official figures.