Matt Hancock has appeared to rule out hugging relatives and friends at Christmas, as he said there are “promising signs” the current lockdown in England is working.
The Health Secretary said rules will still need to be in place over the festive period, with people observing social distancing as families come together.
It comes as Metropolitan Police Commissioner Dame Cressida Dick told LBC radio the police would break up house parties but had “no interest in interrupting family Christmas dinners.”
She added: “The police have lots of other things to be doing.”
Speaking on Times Radio, Mr Hancock said discussions with the devolved nations are continuing with the aim of reaching agreement on how families can celebrate the festive period.
He said there is a need to “respect the fact that we mustn’t spread the virus further but also respect the fact that Christmas is a special time where people get together, especially with their families”.
Mr Hancock added: “It’s about getting the balance right and allowing people to have a Christmas that undoubtedly will be different this year but still try to have that cherished Christmas with your family as much as possible.
“What we want to have is a set of rules that is, if at all possible, consistent across the four nations of the UK, not least because so many people travel to see their family at Christmas time, but also respects the fact that we must follow social distancing to keep the virus under control.
“I’ve got no doubt that people will continue to respect social distancing throughout, because we know that that is so important for full control of the virus.”
Speaking on BBC Breakfast, Mr Hancock said this Christmas “won’t be fully normal”, adding “there will have to be rules, unfortunately, to keep the virus under control”.
But he told BBC Radio 4’s Today programme that while 2020 has been “such a difficult year”, there are signs the current lockdown in England is working.
“There are promising signs that we have seen a flattening of the number of cases since lockdown was brought in and that is good news, though clearly there is further to go,” he said.
“I’m calling it a flattening rather than a fall because one swallow doesn’t make a summer, but there are promising signs that lockdown is working to get the number of cases under control.”
Dismissing the idea that it should be up to families to decide their own rules for Christmas, Mr Hancock said people could pass the virus on without knowing it.
But he added: “Christmas is a special time of year and we’ve had such a difficult year in 2020 – it has been such a terrible year and having some hope, some joy at Christmas, I know that would be welcomed by so many people.”
Earlier, Wales’s First Minister Mark Drakeford said he had held discussions with Cabinet Office minister Michael Gove and the first ministers of the other devolved administrations on Wednesday about a UK-wide approach to Christmas restrictions, with another meeting planned next week.
“We agreed some broad parameters on Wednesday and remitted officials of all four administrations to work now on the detail, so I remain hopeful that it will be possible to reach a four-nation approach to Christmas,” he told the Today programme.
Chris Hopson, chief executive of NHS Providers, said it was “still too early to tell” if the current lockdown will have the “consistent effect” needed.
In a blog post calling for the NHS to be protected, he added: “There is a real risk that in our desire to celebrate Christmas, we swap a few days of celebration for the misery of a full third wave a few weeks later.”
But Calum Semple, professor of child health and outbreak medicine at Liverpool University and a member of the Scientific Advisory Group for Emergencies (Sage), which advises the Government, said there is reason for optimism that the national lockdown in England will push Covid case numbers to a low level before Christmas.
He told Today there is “encouraging evidence coming from the north-west of England” with “a plateauing of cases in the community and a slight downturn in cases coming into hospital”.
He added: “This gives us great optimism that, with lockdown on top, we will be seeing overall numbers in the country driven down, so there is a lot to be optimistic about, along with the coming of a vaccine.”
However, he stressed “some parts of the country really are in a very difficult situation at the moment and their cases are still rising”.
On Friday, the Office for National Statistics (ONS) said there were “substantial differences” in Covid-19 infection rates across England.
Data from November 8 to 14 suggests the overall national infection rate for England is similar to the week before, but there are stark regional divides, with rising rates in primary school aged children.
The ONS said infection rates have continued to increase in London, the East of England and the South East, but appear to be decreasing in the North West and the East Midlands.
Sage said the reproduction number – or R value – for the whole of the UK had dropped to between 1 and 1.1.
Earlier, Professor Sir David Spiegelhalter, statistician at the University of Cambridge, told Today he fears mixing at Christmas could lead to “tens of thousands” more Covid cases, requiring an extra clampdown.
“It is quite plausible that a few days of relaxing would lead to tens of thousands of more cases and that means extra deaths and measures needed to bring those under control,” he said.
Professor Neil Ferguson, of Imperial College London, has also warned restrictions may need to remain in large parts of England after December 2 to stop infection levels rebounding immediately.
The epidemiologist, whose modelling led to the original lockdown in March, told The Guardian that infection rates appear to be “plateauing” and may be starting to go down slowly.
He added: “A halving of infection prevalence over the four weeks would be a positive result.”
Regarding vaccines, Mr Hancock confirmed volunteers are currently being trained but the “big numbers” in terms of vaccinating people will be in the new year.
He told Today: “We’ve changed the law to change the number of clinically qualified people who can vaccinate because this is going to be one of the biggest civilian projects in history.”