Snow has started hitting parts of the UK, with other areas being warned of potential flooding.
South-east England will see a mix of snow, sleet and rain on Monday, BBC Weather says.
The Met Office has warned of ice and snow across southern England and Wales from Monday afternoon, which could cause travel disruption.
Flooding could also continue later, mainly in central England, the Environment Agency said.
The Met Office has issued a yellow warning for ice for southern England and southern Wales, from 15:00 Monday until 03:00 on Tuesday. It warns that ice and small amounts of snow “could lead to slippery surfaces in new places” and potentially slower journeys.
BBC Weather forecaster Stav Danaos said north-east England will see light rain, light sleet and snow over hills, while south-east England will experience wintry showers and “a light dusting of snow”, even in lower areas.
The Met Office said “a mix of sleet and snow showers” will move in from the east, with temperatures reaching “near zero”.
“Given these wintry showers, and also wet surfaces after recent wet weather, some icy patches are likely on untreated surfaces,” the forecaster added.
A yellow warning for ice was also issued for parts of Northern Ireland, with the Met Office warning of potentially difficult travelling conditions caused by icy patches on some untreated roads, pavements and cycle paths.
Police have urged road users to exercise caution.
“Stick to main, gritted roads when possible. Slow down, and increase your braking distance from the vehicle in front,” a Police Service of Northern Ireland spokesperson said.
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The UK Health Security Agency (UKHSA) has already issued a cold weather alert covering the whole of England until Friday.
Dr Agostinho Sousa, from UKHSA, stressed the importance of checking on those who could be vulnerable.
For older people in particular, cold weather can increase the risk of heart attacks, strokes, pneumonia and worsening arthritis. There can also be an increase in accidents at home, due to a loss of strength and dexterity in the hands.
Meanwhile, the Environment Agency (EA) has said “significant river flooding impacts” are expected on Monday in parts of the Midlands, Lincolnshire and on the River Thames.
EA flood duty manager Katharine Smith urged people not to drive through flood water, and to follow advice of local emergency services on the roads.
“Flood water is often deeper than it looks and just 30cm (11 inches) of flowing water is enough to float your car,” she said.
The warning follows a week of heavy rainfall last week, some of which came as part of Storm Henk.
The EA warned that more than 1,800 properties have already flooded, and more could be affected over the next week as river levels rise.
Thousands of homes and businesses areat risk of flooding in Surrey due to rising water levels of the River Thames, while an MP in Oxford has said the wait for a flood alleviation scheme is “frustrating”after parts of the city were submerged after Storm Henk last week.
Labour leader Sir Keir Starmer has said the government’s response to flooding is not “good enough”, and said his party would have established a task force earlier in the year to tackle the problem.
“The response wasn’t quick enough. So I just don’t think it’s good enough for the government to come after the event again and express sympathy,” Mr Starmer told reporters on a visit to the East Midlands on Monday morning.
Prime Minister Rishi Sunak visited flood-hit communities and EA workers in Oxford on Sunday, saying that “touch wood, we’re past the worst of it”.
He said the government had invested record figures in flood defences, which had helped to protect homes.