Hundreds of trains are cancelled, many schools are closed and forecasters say some rural communities may be cut off.
Kent, Surrey, Suffolk and Sussex are among the worst-hit counties, seeing 5-10cm of snow, while north-east England has received up to 8cm (3in).
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.
In Lincolnshire, police helped 45 schoolchildren from their bus after it collided with a car and left the road. None of the pupils were injured, but the force said conditions were "particularly hazardous".
The UK is experiencing what's expected to be the coldest week of the winter, with snow moving west during Tuesday, increasingly spreading into Scotland and the Midlands later in the day.
Temperatures dropped well below freezing overnight, with Northern Ireland, south west England and East Anglia logging figures as low as -6C. Altnaharra in the Highlands recorded -8.5C.
By Wednesday night, more than 20cm of snow could have accumulated in some parts of Scotland, eastern England and Northern Ireland.
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.
"It will feel more like -10C or -14C in some parts and there will be heavy snow showers in the East, particularly in north-east England."
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