More than 100 flood warnings have been issued for parts of the south of England, meaning flooding is "expected" in these areas.
More than 260 flood alerts are in place in parts of England and Wales, which mean flooding is "possible".
The Environment Agency said it is monitoring swollen rivers around the UK, with some close to bursting their banks.
It comes after snow and freezing rain swept across parts of the UK over the weekend, bringing cancellations and delays across the transport network.
An amber weather warning has been extended into Monday morning, but now covers a smaller area, spanning parts of Cumbria, Lancashire and the Lake District. Less severe yellow weather warnings are in force for large parts of Scotland, Wales and elsewhere in England.
Several airports were earlier forced to shut their runways, with Manchester and Liverpool able to reopen only on Sunday morning. Delays continued throughout the day.
Amber warnings are more serious than yellow warnings and indicate a possible risk to life, as well as more significant travel disruption.
Temperatures are forecast to dip again from Monday to below average, with "widespread frost and the threat of ice" remaining, the Met Office said.
The agency said some rural communities could be cut off by snow, and some travel delays and power cuts are likely in northern England.
Up to 15cm more snow could fall in those areas, it added.
The lowest temperature recorded over Saturday night was in Loch Glascarnoch, Scotland (-11C), while heavy snow affected much of England and northern Wales.
Bingley in West Yorkshire had recorded 16cm of snow as of 09:00 on Sunday. In the late afternoon, heavy snow was still falling in Cumbria - with around 10cm lying in Shap - in the far north of England, and across southern Scotland.
There was also around 5cm of snow in many cities including Leeds and York, according to BBC Weather.
Manchester Airport faced delays in Sunday after it was forced to close its runways, and urged passengers to check with their airline for updates on their flight.
As a result of heavy snowfall overnight, Liverpool, Bristol, Birmingham, Newcastle and Leeds airports also temporarily closed their runways. All have since reopened.
Stuart Irons, from National Highways, told BBC Breakfast on Sunday that 500 gritting lorries planned to be out across the UK and they had stockpiled more than 240,000 tonnes of salt.
In Merseyside, two safety meetings were held on Sunday morning to assess whether the snow and travel conditions would affect the Premier League clash between Liverpool and Manchester United, but the match was given the go-ahead.
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