December is on course to be the coldest since records began in 1910, the BBC weather centre has said.
Christmas Day was extremely cold in much of the UK and fresh snow fell in Aberdeen, Glasgow and Edinburgh, making it a white Christmas in those areas.
The Highways Agency has urged drivers to take care in difficult conditions.
BBC forecaster Peter Gibbs said it would not be as cold in the next few days, although ice is likely in some areas, particularly Northern Ireland.
"Over the next few days milder weather will spread from the west, accompanied by rain, sleet and snow. There is a risk of some icy conditions during that time," he said.
Earlier, BBC forecaster Liam Dutton said December was likely to be the coldest for over a century, while the rest of the country will be dry and bright with patchy freezing fog.
Temperatures stayed below freezing in much of the UK following overnight temperatures which dropped to to minus 17C at Worcester and minus 18C at Altnaharra in northern Scotland.
Members of the Serpentine Swimming Club arrived in London's Hyde Park to find that the annual open-air Christmas Day 100m race had been cancelled.
Undeterred, about 40 people jumped into an area of the lake where the ice had been broken up.
Club secretary Brian Thomas said: "We just went for a quick dip and a wade in the ice. It was chilly but invigorating."
Travellers hoping to get away from for the festive season struggled with reduced train services, frozen roads and delays and cancellations cancellations to flights.
The AA said Christmas Eve call-outs were 40% above normal due to Christmas shopping and the festive getaway.
It estimated that it covered about 13,000 breakdowns by the end of 24 December compared with just over 9,000 on a normal Friday.
On Christmas Eve, police and coastguards were called to help drivers stuck in cars after blizzard conditions affected the Whitby area of North Yorkshire.
Several train companies operated amended timetables, with some services scrapped on the main London to Scotland routes up the east and west coasts.
The RMT transport union said it was "scandalous" that operators could introduce "special" timetables while escaping financial penalties.
British Airways said all its long-haul flights from Heathrow airport, as well as the vast majority of short-haul services, flew as scheduled.
Away from Heathrow, some short-haul flights were cancelled from some other UK airports due to the continuing bad weather in Europe.