As temperatures move above 0C, ice and snow will begin to melt, with localised flooding possible, the Met Office said.
More than 30 flood alerts are in place across England and Scotland.
Southern England could see patchy frost this week (Jordan Pettitt/PA)
Greg Dewhurst, meteorologist for the national weather service, said temperatures will be milder across the country, but there will be a north-south split in conditions.
He told the PA news agency that the most dramatic change in weather will be in Northern Ireland, Scotland and the far north-west of England.
“Cloudy and patchy rain are moving in from the Atlantic and winds will turn south-westerly, bringing in milder air,” Mr Dewhurst said.
Temperatures are set to be well above freezing and will rise overnight into Monday, reaching as high as 10C in Scotland.
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Much of England and Wales will be between minus 1C and 3C overnight, which is not as cold as recent nights, Mr Dewhurst said.
On Monday, Northern Ireland, Scotland and northern parts of England will be cloudy with outbreaks of patchy rain and temperatures between 9C and 12C.
Meanwhile, central and southern areas of England will be drier, with sunny spells and temperatures between 5C and 8C.
There could still be some patchy frost in southern areas, Mr Dewhurst added, as the UK Health Security Agency’s cold weather health alert remains in place until Tuesday.
Amber alerts are in force, meaning a rise in deaths, particularly among those aged 65 and over or with health conditions, is likely, the agency said.
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.
(PA Graphics)
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.
As the week goes on, Tuesday will be similar to Monday, but potentially drier with temperatures between 11-12C in the north of England and 8-9C in the south, around average temperatures for this time of year.
Daniel Bond, flood duty manager at the Environment Agency, said: “Combined rainfall and snowmelt means there is a very low likelihood of minor river flooding across parts of the Yorkshire and Humber region on Monday and into Tuesday.
“Environment Agency teams continue to be out on the ground, operating flood defences, taking action to reduce the impact of flooding, issuing flood warnings and supporting those communities affected.”