The Met Office said the week is likely to see a split across the country, with warmer temperatures in the south of England and some brighter weather a possibility in the east.
Fog is forecast for the north of England and parts of Scotland, with the potential for brief downpours on Monday.
Meteorologist Sarah Kent said cloud cover is likely to be extensive in parts of the UK on Christmas Day itself, with temperatures ranging from highs of up to 9C or 10C (50F) in the South West, down to 4C (39F) in the North East and 1C (34F) in Glasgow.
Large swathes of the country remain under cloud or fog for much of Boxing Day.
Miss Kent said: “People looking for the sun are probably not going to manage it, I’m afraid.
“It’s really going to be a good old-fashioned day for staying in with a book rather than outside in the weather.”