Many of these have had their power restored, however EDF said its engineers' efforts were being hampered by the bad weather and some 1,200 customers living in and around Colchester, Cambridge, Kings Lynn, Norwich and Ipswich were likely to be without power going into Friday night.
About 200 drivers on the M20 and M2 in Kent were stuck in tailbacks overnight into Friday morning.
Essex Police dealt with more than 180 weather-related incidents during the night, including more than 20 road collisions.
Suffolk Police said it was a "horrendous night". They dealt with 230 incidents after up to 15cm (6in) of snow fell in the county, and dozens of drivers were forced to spend the night in their cars.
Hertfordshire Police had more than 400 emergency calls through the night.
The AA, the UK's biggest breakdown organisation, said it had been a busy night and morning, with breakdowns coming in at a rate of 1,500 every hour.
It estimates it will attend up to 14,000 call outs by the end of Friday, up from an average of 8,500.
• Sections of the M40 were closed during rush hour following accidents. Normal traffic conditions were expected to resume from 1030
• In Essex, more than 70 lorries got stuck in blizzards on the A120 near Harwich, and on the A12 near Colchester some drivers had to sleep in their vehicles until gritters and snowploughs arrived
• Roads in Norfolk, Suffolk and Cambridgeshire were reported to be hazardous
• Other roads affected include the M2 and M20 in Kent, and the A168 in North Yorkshire - partly closed northbound due to a jack-knifed lorry
• Between 30 to 40 cars were trapped behind two lorries, stuck on the A166 in East Yorkshire
• National Hunt racing at Ascot on Friday and Saturday has been abandoned due to 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.
The Met Office said the heaviest snowfall overnight was in Norfolk, Bedford and Buckinghamshire.
Up to 20cm (8in) has fallen in some parts of North Yorkshire but there have been no reports of major traffic problems.
Snow also fell in parts of the Brecon area of mid Wales and in the Neath area of south 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.
The Met Office says there is a risk of heavy snow in north and western Scotland, Northern Ireland, north-west England and northern Wales on Sunday.
However, it 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, which looks after motorways and trunk roads in England, said its gritters and snow ploughs were out mainly in north-east, east and south-east England.
"The majority of the agency's motorways and major A roads remained fully open overnight, however where incidents did occur we worked, where necessary, with the emergency services to reopen the roads as quickly as possible," a spokeswoman said.
Road users had to "play their part" and "drive appropriately", she added.
LATEST BBC TRAVEL NEWS
This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.