Ministers have been meeting to discuss how to contain the rising number of coronavirus infections in England.
It comes as Prime Minister Boris Johnson said he is “hoping to avoid” another national lockdown in England.
But analysis suggests the R number – which represents how many people each infected person passes the virus onto – has risen above 1 in the UK.
Health bosses have warned the NHS is under significant pressure, with nearly 90% of hospital beds in England full.
Government scientists are continuing to evaluate the spread of a new variant of Covid in south-east England as there are “growing concerns” about its transmission.
Prof Sir Mark Walport, a member of the government’s Scientific Advisory Group for Emergencies (Sage), told the BBC’s Newsnight programme there was a possibility the new strain could have a “transmission advantage”.
“We know that this is a new variant, it has been seen in other countries but it seems to be quite widespread which suggests that it has got a transmission advantage,” Sir Mark said. “It does definitely seem possible that this transmits more easily.”
On Monday, Health Secretary Matt Hancock said the variant may be associated with the faster transmission of the virus in the South East but there was “nothing to suggest” it caused worse disease or that vaccines would no longer work.
Ministers have been discussing what action will be necessary to deal with it, but a Downing Street source said the government is “not there yet” on rethinking Christmas plans.
The decision by all four UK nations to relax restrictions and allow more household mixing for five days over Christmas has prompted concerns about a further surge in case numbers.
Christmas rules are due to be relaxed between 23 and 27 December.
But the prime minister has urged people to think about elderly relatives to “avoid spreading the disease” over the holiday period.
Labour leader Sir Keir Starmer has called for Mr Johnson 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”.
Sir Mark Walport told Newsnight the new year would be a difficult time.
“We are going into January in quite a serious situation where we do need quite strong measures to socially distance and if the virus is changing then that makes it even more imperative,” he said.
Meanwhile, tier three Covid rules have come into force for parts of southern England, meaning that 38 million people – more than two-thirds of the nation’s population – are now subject to the toughest restrictions.
The changes, which came into effect at 00:01 GMT, see Bedfordshire, Buckinghamshire, Berkshire, Hertfordshire and parts of Surrey, East Sussex, Cambridgeshire and Hampshire join the list of areas now in the highest level of England’s three-tier system.
In tier three, pubs and restaurants must close and different households cannot mix indoors or in most outdoor venues.
On Friday, the UK recorded a further 28,507 cases, along with 489 deaths within 28 days of a positive test.
Official figures show Covid-19 cases have risen in the past week in England, driven by sharp increases in London, as well as rises in the South East and East Midlands.
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.
The R number is estimated to be between 1.1 and 1.2, up from between 0.9 and 1 last week.
Elsewhere in the UK, a tough new six-week lockdown has been announced in Northern Ireland from 26 December.
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.
Scotland’s Health Secretary Jeane Freeman said the option for a post-Christmas lockdown in Scotland “remains on the table”.