Suffolk Police say it has been an "horrendous night" with lots of people spending the night trapped in their cars. The worst affected area was the A12 between Copdock and the Essex border.
Hertfordshire Police received more than 400 emergency calls through the night.
Conditions are expected to be at their worst in much of the UK during the Friday morning rush hour.
Scores of jacknifed lorries and abandoned cars litter the roads in the worst affected areas. Thousands of children are starting their Christmas holidays a day early as schools in many counties have been forced to close.
Specific incidents include:
• A lorry jackknifed on the A21, near Tunbridge Wells, leaving motorists stuck in the snow for three hours
• A 20mph speed limit was put in place on parts of the M1 overnight
• The A1081, which is the main road connecting Luton Airport to the M1, was gridlocked in the early hours of Friday due to the large number of jackknifed vehicles
• A jacknifed lorry and several other vehicles have also closed part of the M40 between junctions six and four
• Some flights in and out of Heathrow, London City, Luton and Gatwick have already been diverted or cancelled.
TV presenter Davina McCall was among those stuck on the A21 in Kent for three hours after a lorry blocked the road.
She told BBC Radio 5Live: "We got wedged in a whole series of cars and it was pelting down with snow."
Driving winds and sub-zero temperatures brought blizzard conditions to much of the UK late on Thursday and in the early hours of Friday.
BBC Weather forecaster Sarah Keith-Lucas said: "We have already seen snow arriving across south-east and north-east England."
She said the worst affected areas in south-east England were Greater London, Medway and parts of Kent, which are seeing "extremely heavy snowfall".
Met Office severe warnings for heavy snow have also been issued for Yorkshire and Humber.
Up to 20cm (8in) has fallen in some parts of North Yorkshire but there have been no reports of traffic problems.
Some 10cm of snow fell on Thursday night in parts of East Anglia, which made driving treacherous.
The Met Office said the heaviest snowfall overnight was in Norfolk, Bedford and Buckinghamshire.
And a second band is causing severe problems across the Thames Estuary, North Kent and Surrey.
Snow also fell in the Brecon area of mid Wales and in the Neath area of south Wales.
Meanwhile, high winds caused snow drifts to form in parts of Cambridgeshire.
Snow is also forecast in parts of central and northern England, Northern Ireland, Scotland and Wales.
Conditions in the south east of the country are expected to ease during Friday, with more cold and icy weather predicted for Saturday and Sunday.
Further snow is predicted over the weekend, particularly across the north of the UK.
However, the Met Office said it was too early to say whether there would be a white Christmas.
A Met Office spokesman said: "Current indications show an ongoing battle between the colder air currently over the UK and milder air pushing in from the west. As a result the forecast for Christmas Day is still too close to call."
The Highways Agency said it had 94 winter maintenance compounds across England, with 25 in the south-east, and was able to treat all roads within three hours of severe forecasts.
A spokesman told the BBC road users had to "play their part" and "drive appropriately".
"We are asking drivers to carry out simple vehicle checks before they set out; to carry a severe weather emergency kit in their vehicles and to monitor the traffic and weather conditions," he said.
Earlier this week, the AA motoring organisation said half of the UK's local authorities only had enough road salt for six days of continuous freezing.
It said councils had 250,000 tonnes less salt than a decade ago - a claim dismissed as "scaremongering" by the Local Government Association.
Have you been affected by the snowy conditions? Let us know using the form below. You can also send in your snow pictures and video.
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