A north-south divide is set to emerge with milder temperatures in the North but cooler conditions in the South.
Temperatures will reach 12C or 13C in northern areas on Tuesday, causing snow to thaw, the Met Office said.
In the South, there will be a more gradual recovery from the cold snap, with temperatures staying at around 8C.
It will be cloudy for the vast majority, but some sunshine is possible in southern coastal districts of England and eastern areas of Scotland, the forecaster said.
Northern and western areas of the country could see some rain and drizzle as the week goes on.
Met Office Spokesperson Andrea Bishop said: “There’s a north-south divide this week, with temperatures significantly milder across the north, with a more gradual recovery in the south.
“This will bring some thawing of lying snow in the north and some rain, whilst it will largely be drier in the south.
“After a very mild night in Scotland and Northern Ireland, we could wake to see some patchy frost in the south on Tuesday morning.
“The best of any sunshine will be on southern coastal districts of England, although eastern areas of Scotland may also see some brightness, but it will generally be a cloudy day for the vast majority.
“Temperatures will range from 8C in the south to 12C or 13C in the north.
“Northern and western areas see more in way of rain and drizzle this week, but for many of us, it should be a more settled week than of late.
“There is the risk of some mist and fog lingering in more southern areas, which we are keeping an eye on.”
White wintry scenes have been a fixture across the country so far this year, with flooded fields frozen over, and frost and snow making for picturesque views.Temperatures plummeted to minus 18.9C on Saturday morning in Altnaharra, Scotland, and it was the UK’s coldest January temperature in 15 years.
The average low in northern Scotland for this time of year is about 0.3C, while for England, overnight lows are about 1.5C to 1.6C.
More than 30 flood alerts were in place across England and Scotland on Monday, due to fears that the thaw could lead to some flooding.
