Schools are closed, hundreds of trains are cancelled and conditions on some roads are “treacherous”.
Drivers are being warned of hazardous conditions on roads as heavy snowfall hits parts of the UK.
Three people died following a crash in Lincolnshire while one man died in a crash in Cambridgeshire. Police have not said if they were weather-related.
Hundreds of trains are cancelled, many schools are shut and forecasters say some rural communities may be cut off.
Kent, Surrey, Suffolk and Sussex have seen up to 10cm (4in) of snow, while north-east England has had up to 8cm.
Amber Met Office weather warnings are in place in those areas, meaning there is a possible risk to life and property.
A less severe yellow warning applies to a much wider area, covering much of Scotland, England and Wales.
Lincolnshire Police say three people died following a crash at about 06:15 GMT on the A15 near Baston.
Officers have not said whether the crash – which involved a blue Renault Clio and a white lorry – was caused by the poor weather, but the force said earlier that roads in the county were “particularly hazardous”.
Lincolnshire County Council said the road had been gritted in the early hours of Tuesday morning.
A man also died following a three-car collision on the A47 near Peterborough, while a 17 vehicles were involved in a crash on the A120, in Essex.
Officers in Lincolnshire also helped 45 schoolchildren from their bus after it collided with a car and left the road. None of the pupils was injured.
The UK is experiencing what is expected to be the coldest week of the winter, with snow moving west during Tuesday, spreading into Scotland and the Midlands.
Up to 40cm (15in) of snow could fall in north-east England and Scotland, between Wednesday morning and Thursday lunchtime, the Met Office says.
Temperatures dropped well below freezing on Monday night, with Northern Ireland, south-west England and East Anglia logging figures as low as -6C. The lowest temperature was -8.9C and was recorded in Farnborough, Hampshire.
It is expected to get as low as -15C by midweek in areas where snow has fallen.
Scotland’s transport minister Humza Yousaf warned an amber warning in place for parts of the country could be upgraded to the most serious red warning – meaning “extreme weather is expected”.
BBC Weather meteorologist Gemma Plumb said: “On Wednesday and Thursday it is going to feel bitterly cold with a lot of areas seeing maximum temperatures below freezing.
“There will be heavy snow showers in the East, particularly in north-east Britain.”
Among the disruption on Tuesday:
Network Rail said it was working to restore rail services in East Anglia, after conditions there had not been as bad as expected.
Some lines had been closed in advance of forecasted snow in the area, with engineers asked instead to focus on keeping the main lines open.
Apologising, Meliha Duymaz, from Network Rail Anglia, said the weather had not been as bad as anticipated, and a full service was expected on Wednesday.
#UKSnow – There are amber and yellow weather warnings for snow and ice across England, Scotland and Wales this week. Disruption to your train journey may continue today, tomorrow and Thursday. Full details and the impact to your journey can be found here: https://t.co/JdnzicooXs
Motorists, meanwhile, are being urged to take extra care and in the worst affected areas, only travel if really necessary.
The RAC’s Pete Williams advised drivers to check fuel levels, oil, tyre tread and pressure, coolant, lights and screen wash before setting out.
Hundreds of schools across the UK are shut, particularly in north-east England, Yorkshire, and the South East.
Closures have also been announced in north-west England and northern and eastern Scotland, and in north Wales more than 230 are shut.
At least 238 schools and nurseries have shut in Kent, as well as others in Sussex and Surrey.
Emergency shelters have been opened across the country as councils offer extra accommodation to the homeless during the freezing conditions.
The offer of a hot shower, clean clothes, food and a bed can help save lives, homeless charity St Mungo’s said.
Weather warnings are expected to be in place until Friday.
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Police warn of hazardous road conditions as officers deal with a number of serious crashes.