Health Secretary Matt Hancock has said that Christmas was "the most important holiday for people in this country", and that a consistent set of rules was needed so that families could enjoy celebrations together.
Speaking on Times Radio he said that there had been lots of debate about how to handle the festive period "in the age of coronavirus".
"What we're trying to do is ensure that we have a set of rules across the whole UK, so there's talks going on with the devolved authorities to try and agree a common set of rules," he said.
"...to make sure we 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.
"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."
Mr Hancock added that the Government wanted the rules to be "consistent across the four nations of the UK" and that he had "no doubt" people would continue to respect the rules.
First Minister Mark Drakeford said there was evidence that the firebreak in Wales had successfully had an impact on lowering the rate of coronavirus transmission.
It comes as Northern Ireland announced its own firebreak-style lockdown, due to start next week. The lockdown has put a restriction on churches. They will only be allowed to open for weddings and funerals, with up to 25 people in attendance at any one time from next Friday.
Drakeford said he had held discussions with Cabinet Office minister Michael Gove and the other first ministers of the devolved administrations on Wednesday about a UK-wide approach to Christmas restrictions, with another meeting planned for next week.
He told BBC Radio 4's Today programme. "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.
"I certainly think that is the right thing to do - if it is achievable - and certainly Wales will be at the table next week looking to find an agreement."
Mr Drakeford said an agreement on permitting travel across the UK during the Christmas season was "top of the list of things to agree", even if a wider agreement was not possible.
"I really do hope we can have a common approach to travel," he added.
"It is very important for people in Wales, so many families here will have families in England and elsewhere and will be hoping to have visits from family members who live outside Wales. On travel, I am more hopeful than I was even on other aspects of our discussion."
Meanwhile, Britain's most senior police officer has said she has "no interest in interrupting family Christmas dinners" to catch Covid-19 rule breakers.
Speaking during an LBC radio phone-in on Friday, Metropolitan Police Commissioner Dame Cressida Dick said the force will "work with whatever the Government say are the current restrictions".
But when asked by host Nick Ferrari whether her officers would "bang on the door and count the number of people eating the turkey" during the festive period, Dame Cressida said police do not have the authority to enter people's homes to enforce coronavirus legislation.
"We have no powers of entry," she said.
"I have no intention in any way of encouraging my people to be barging through people's doors or knocking on people's doors unless you've got, as we sometimes do - and then they can't barge, they may knock - a huge party going on, which is clearly very, very dangerous and causing lots of concern with the neighbours.
"Well then we might be knocking on the door saying, 'you need to stop this'."
Reports suggest households might be allowed to mix indoors for a five-day period from Christmas Eve, and that ministers are considering plans to allow three or four households to form bubbles.