Some properties in Sussex have been without power since Tuesday night.
EDF Energy says its engineers are finding it difficult to reach the villages because of the freezing roads. Some homes in Surrey have also been affected.
Meanwhile, an eight-year-old boy has been airlifted to Nottingham for a kidney transplant after he and his father got stuck in snow trying to reach the QMC Hospital.
They set off from Gainsborough in Lincolnshire on Wednesday morning after hearing an organ was available.
In various parts of southern England, coastguard services using 4X4s are helping ambulances to get paramedics into hard-to-reach areas.
The military was called in after hundreds of vehicles were stranded when snow blocked the A3 in Hampshire overnight.
The Met Office said between 35cm (14in) and 40cm (16in) of snow had fallen in some parts of southern central England.
Snow depths taken around the UK include 47cm (19in) in Aviemore, 19cm (7.5in) at Brize Norton in Oxfordshire, and 17cm (7in) in High Wycombe, Buckinghamshire. Temperatures of -10C (14F) in rural areas - and even as low as -20C (-4F) in parts of Scotland - will cause snow to freeze, making for treacherous driving conditions.
Gatwick Airport has now re-opened after being closed on Tuesday evening, and Cardiff Airport has limited services. Heathrow, Birmingham, Luton, Glasgow and Southampton are open but suffering delays and cancellations.
Stansted Airport in Essex closed around 1000 GMT but reopened around midday. Bournemouth, Jersey and Bristol airports have also reopened but Aberdeen Airport has closed to clear snow from the runways.
More than 8,000 schools closed their doors on Wednesday, and some plan to remain closed on Thursday.
More than 1,000 have shut in Wales, and the same number in the West Midlands. About 450 in Devon and Cornwall have shut, 500 in Hampshire, Dorset and Isle of Wight, and 400 in the Somerset area.
Hundreds more have closed in Herefordshire, West Yorkshire, Lancashire and north-east England.
First Minister Alex Salmond said the weather in Scotland was now at its worst since 1963.
He said 45,000 tonnes of salt and grit were available there, enough for only 10 days in a normal winter. These supplies will be replenished but will be used for main roads, because more snow and sub-zero temperatures have been forecast.
All schools in central Borders, East Lothian and Midlothian, Shetland and Aberdeenshire are so far closed, as well as half the schools in Dumfries and Galloway.
WEATHER AND TRAVEL INFO
Get the latest on school closures and travel problems via your
On the roads, the Highways Agency said the A66 in Cumbria was also shut between the A1 and the A685.
Police in the Borders said conditions were so bad that people should avoid travelling.
Supplies of road grit and salt are running low, according to many councils, with only major roads being treated in several places. Restrictions on lorry movements to and from the Winsford mine in Cheshire, the UK's biggest rock salt mine, have been eased to help meet a huge demand for salt.
At 1400 GMT, Cheshire Police said there were about 100 lorries waiting to get into the salt works, causing tailbacks in nearby towns.
Sand from the beach at Scarborough is being used by council workers to grit pathways in the town.
AA spokesman Donald MacSporran said breakdown crews were struggling to get to stranded motorists because their vehicles were "no better at getting through snow than any other modern car".
Police worked with the armed forces and fire service in Hampshire, using military trucks and Land Rovers to get to motorists stranded on the A3(M).
TV presenter Annabel Giles was among the hundreds of drivers stranded there. She was stuck in her car on the A3 for more than 22 hours en route to Brighton.
She told the BBC News website: "You can't sleep because the traffic keeps moving on a couple of inches and everyone starts beeping their horns and you have to wake up and get into gear and move on".
The UK is in the grip of its longest cold snap for almost 30 years, and extreme or severe weather warnings are still in place across the UK for both snow and ice.
The current lowest temperature recorded during this freeze is -18C in Braemar, Aberdeenshire, on 29 December. The lowest ever in the UK is -27C.
In Wales there was heavy snowfall overnight, particularly in the south, with 15cm (6in) at Sennybridge, near Brecon, and unconfirmed reports of 30.5 cm (1ft) at Newtown in Powys.
About a dozen mountain roads have been closed because of the snow.
Among other developments:
• National Rail Enquiries have set up a special number for information about trains affected by the weather, on 08453 017 641
• East Midlands Trains between Sheffield and Leeds were cancelled
• All First Bus services in Bristol, Bath and Somerset have been cancelled because of heavy snow
• More than 120 flights have been cancelled at Heathrow Airport
• Hampshire County Council hired 120 farmers and contractors to help clear the road using their machinery.
• Other major roads affected by closures included the A628 in South Yorkshire and Derbyshire, the A30 in Devon
• Honda and BMW's Mini shut their plants in Swindon and Oxford respectively because of the bad weather
• Sections of main roads including the A1, A616 and the M1 in South Yorkshire were closed.
• All outpatient appointments and non-urgent operations at the hospitals covered by the Oxford Radcliffe Hospitals Trust will also be postponed on Thursday.
The Association of Train Operating Companies said trains were worst affected in London and the South East, where most operators are running reduced services.
SNOW TRAVEL ADVICE
If your journey is not essential, wait until local conditions improve.
If you are driving, check the weather conditions before you set out.
Listen to travel bulletins on the radio.
Take spare warm clothes, food, water, boots, a torch and, if you have one, a spade with you.
Make sure there is enough braking and stopping distance between your car and the next.
Be careful even after road surfaces have been treated with salt.
Source: Highways Agency
Train operators running revised timetables include East Coast, East Midlands, Chiltern Railways, First Great Western, Arriva Trains Wales, National Express East Anglia, South West Trains, Southeastern, Southern and First Capital Connect.
Transport for London said a good service was operating on most Tube lines and buses.
But commuters on train services out of the capital are being warned of serious disruption on Wednesday night, with some trains out of Victoria and Charing Cross finishing as early as 2015 GMT to some destinations.
Several hospitals across the UK, including some in Wiltshire and Surrey have cancelled most of their outpatient appointments to focus on emergencies.
Reading's Royal Berkshire Hospital has sent midwives out in 4x4s to help a number of women in labour.
Wednesday's Carling Cup semi-final between Manchester City and Manchester United has been postponed, as has the Barclays Premier League match between Arsenal and Bolton at the Emirates Stadium in London.
Horse racing has been abandoned at Huntingdon and Ludlow on Thursday.
Friday's National Hunt meeting at Bangor has been scrapped, as has Saturday's fixture at Wincanton and Sunday's race at Hereford.
Why the cold weather?
The current big chill is a result of high pressure over the polar region, which has pushed cold air out of the Arctic towards much of northern Europe, parts of Asia and the US. Winds from the north and north east, rather than the south and south west, have brought freezing temperatures to the UK.
Provisional Met Office figures for December show temperatures for much of the UK were 1.5C and 2.5C below the mean temperatures for the last 30 years. Scotland saw temperatures dip still lower - from 2.5C to 3.5C. On Thursday, temperatures in Scotland plunged to -22.3C in places.
Winds from the north also brought cold weather to parts of Asia, with Beijing receiving its heaviest snowfall for nearly 60 years. At the weekend, up to 30cm (12in) of snow fell in China's capital and its neighbouring port city of Tianjin. Dozens of people have also died in a cold snap in northern India.
However, while parts of the world suffer freezing temperatures, the seesaw patterns mean other areas are warmer than usual, including Alaska, northern Canada and the Mediterranean. Met Office figures for the end of 2009 show some places dropped 10C below the average, while others were 10C above.
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