Temperatures are forecast to rise to double figures on Monday, though the end of the bitter cold snap could bring some flooding.
Ice and snow will begin to melt as temperatures rise above 0C (32F), with localised flooding possible, the Met Office said.
At least 30 flood alerts and two flood warnings are in place across England.
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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.”
Temperatures will be milder across the country but there will be a north-south split in conditions, meteorologist Greg Dewhurst said.
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Northern Ireland, Scotland and the far northwest of England will see the most dramatic change in weather, he said.
“Cloudy and patchy rain are moving in from the Atlantic and winds will turn southwesterly, bringing in milder air,” Mr Dewhurst said.
Temperatures will rise overnight into Monday, reaching as high as 10C (50F) in Scotland.
Much of England and Wales will be between -1C (30F) and 3C (37F) overnight – not as cold as recent nights, Mr Dewhurst said.
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Parts of England, Northern Ireland and Scotland will be cloudy with outbreaks of patchy rain and temperatures between 9C (48F) and 12C (54F) on Monday.
But central and southern areas of England will be drier, with sunny spells and temperatures between 5C (41F) and 8C (47F).
Mr Dewhurst added there could still be some patchy frost in southern areas.
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The UK Health 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.
It comes after the UK’s coldest January temperature in 15 years, as temperatures plummeted to -18.9C (-2F) on Saturday morning in Altnaharra in Scotland.
Tuesday is forecast to be similar to Monday, but potentially drier, with temperatures between 11-12C (52-54F) in the north of England and 8-9C (46-48F) in the south.
