More freezing temperatures and snow flurries are predicted for February.
Icy winds heading for the UK will make temperatures feel "sub zero" as the coldest winter in 13 years continues.
Snowstorms from Russia are expected to hit the eastern part of England on Sunday night.
Night-time temperatures are set to drop to -2C (28F) as a blast of cold air sweeps in from the North Sea.
Bitterly cold easterly winds will cause snow to drift, with forecasters predicting that 5cm to 10cm will fall over many parts of England and Wales.
Snow showers are likely to be less widespread in Scotland and Northern Ireland.
On Saturday, winds began gusting at up to 70mph over the hills of northern Britain and snow could fall as deep as 20cm over high ground in the coming days.
The first wintry showers are expected on Sunday night and they are likely to become much more widespread by Monday.
'Flirting with hypothermia'
Alex Deakin, from the BBC Weather Centre, said: "Temperatures during the day will reach one or two degrees above freezing but with the significant wind chill it will feel sub-zero everywhere."
He added drivers should take extra care with the weather likely to cause problems throughout Monday.
Slightly milder air will move in during Tuesday, with snow mainly confined to hills.
The AA has warned drivers to keep extra clothes in their car to make sure they are prepared for the cold snap.
Patrolman Andy Taylor said: "People often treat their car as an overcoat. But when you break down you are suddenly vulnerable to the weather.
"If you break down on a motorway, the safety advice is to get out of the car and wait behind the barrier. Unless you have extra clothes you really are flirting with hypothermia."
With a freezing start looking likely for February the season could be the coldest since 1995/1996, when a temperature of -27.2C (-17F) was recorded in the remote Scottish village of Altnaharra, equalling the UK's national lowest temperature.
Roads could be plagued by snow at the start of the week.
So far this winter temperatures have been between 1 and 1.5C below average. At the beginning of January they plunged to lows of -13C (9F). Dozens of schools were closed and thousands of homes were without water.
In Sandbanks, in Dorset, the sea partially froze, the first time it has happened on the South Coast since 1991.
The extreme temperatures came as cold Arctic air was dragged across the country from the north, lingering for more than a week because high pressure prevented it from moving away.
January has been a drier month compared to previous years. The average rainfall was 100mm, just under last year's figure of 130mm. Forecasters say February is expected to be fairly similar.
"February is not looking like a wet month. Wet weather is usually dominated by the Atlantic but at the moment it is looking like weather patterns from the east and north will dominate," said Michael Dukes, senior forecast manager of MeteoGroup.
The cold snap at the beginning of the year triggered extra cold weather payments for millions of pensioners and vulnerable people.
The £25-a-week assistance comes into force when an area's average temperature falls or is forecast to fall to 0C or below for seven consecutive days.