People are being warned to avoid non-essential travel
Britain is bracing itself for further disruption as fresh bands of snow sweep across parts of the country.
South-east England has been hit by the heaviest snow in 18 years, causing trains and buses to be cancelled, and airports and schools to be closed.
Snow is now moving north, with the Pennines, north-east England and the Scottish Borders at risk of seeing up to 12 inches (30cm) of snowfall.
The Met Office has issued an extreme weather warning for much of the UK.
As well as heavy snow in many areas, there is a risk of widespread ice in London and south-east England as temperatures fall as low as -7C overnight.
The ice could make road travel treacherous and pavements hazardous, although conditions may ease slightly later on Tuesday with temperatures expected to hit 4C or 5C in some places.
At a press conference in Downing Street on Monday, Prime Minister Gordon Brown said: "We are doing everything in our power to ensure services, road, rail and airports are open as quickly as possible, and we are continuing to monitor this throughout the day."
A snowman greeted BBC website reader David Shipway on his doorstep
Weather forecasters said the worst-affected area on Monday had been the Thames Valley and Greater London, where the transport network is at its most concentrated.
Some parts of London saw up to eight inches (20 cm) of snow.
The BBC's Alex Deakin said northern England, especially the Pennines, could see between four and 12 inches (10 and 30cm) on Tuesday, with up to eight inches (20cm) in eastern Scotland and the Borders.
Strong winds could make conditions worse in these areas, causing snow to drift.
Snow will also continue across south Wales and south-west England, and spread into Northern Ireland, our forecaster said.
More snow is likely in northern Scotland on Wednesday, he added.
DEPTH OF SNOW AT 0900 GMT
North Downs: 11 inches (28cm)
London: 8 inches (20cm)
Berkshire: 6 inches (15cm)
East Anglia: 4 inches (10cm)
Midlands: 2 inches (6cm)
Northern England: 2 inches (6cm)
The Met Office said it expects the rest of the winter to continue to be colder than average.
Thousands of children missed lessons on Monday as more than 3,000 schools across the UK were closed for the day.
Many are expected to remain closed on Tuesday, including all schools in Birmingham, Bradford and the Borders, and all 403 state schools in Surrey.
Travel disruption is also set to continue. The BBC's Tom Symonds said trains in East Anglia and on the East Coast Mainline between London and Edinburgh could be worst hit on Tuesday.
A limited rail service is set to resume south of London.
Hospitals in London asked extra staff to come into work because of an increase in 999 calls on Monday.
London Ambulance Service is running a reduced service and its assistant chief ambulance officer, John Pooley, said its staff were under a great deal of pressure.
The Federation of Small Businesses estimates almost 6.5m people - a fifth of Britain's workforce - took the day off work as a result of the weather on Monday.
It also believes that three days of disruption caused by snowfalls will cost the economy about £3.5bn.
Several London theatres cancelled performances and many offices sent staff home early.
All flights at London's Heathrow Airport were cancelled until 1700 GMT and customers whose flights had been cancelled were advised not to go to the airport.
London City and Luton airports are closed. Norwich and Leeds Bradford airports have now re-opened.
BAA has warned passengers travelling to and from Heathrow, Gatwick and Stansted airports to expect "significant delays and cancellations".
Heathrow cancelled almost 800 flights on Monday.
BMI, Heathrow's second largest airline, has cancelled all flights to and from the airport.
Heathrow Express rail services have been suspended, while Heathrow Connect, Gatwick Express and Stansted Express are operating a limited service.
On the roads, motorists have been warned of dangerous driving conditions.
The Highways Agency is continuing to warn drivers not to travel unless their journey is essential. "If you do have to travel, be prepared," a spokeswoman added.
There have been a string of accidents on many motorways and A roads, causing road closures, long delays and vehicles to become stranded.
And there was more bad news for people trying to use public transport in the South East of England.
All London buses were withdrawn from service on Monday morning due "to adverse weather and dangerous driving conditions". About 100 routes, mainly into and out of central London, have been re-introduced but most are still not running.
Services are operating on more than 80% of the Tube network, although many lines remain partially suspended with the Circle line entirely suspended.
South West Trains is running a reduced service on most routes and passengers are advised not to travel unless their journey is essential.
David Brown, of Transport for London, said the situation was "exceptional".
He added: "We were prepared in the sense that all our cold weather plans on the Underground were put into place.
"But I think that actually the volume of the snow falling during the middle of the night was very difficult for us."
Liberal Democrat shadow transport secretary, Norman Baker said it was "an absolute disgrace" the country's transport networks were unable to cope with bad weather.
"The lack of preparedness is astounding and damaging for the economy. I have travelled from Stockholm to the Arctic Circle on a train that arrived five minutes early, yet Britain lapses into chaos at the first hint of snow," he said.
Edward Welsh, of the Local Government Association, said councils had been "working flat out" since Sunday morning.
"If we had hundreds of gritters on stand-by for a day like this, a day which happens once in every 18 years, we'd have to divert resources from somewhere else," he said.
Eurostar services are currently operating between the UK and the continent, but are subject to possible delays due to the heavy snow in the UK and northern France.
But not everyone has been inconvenienced by the weather - Erik Anderson, from Richmond upon Thames, contacted the BBC News website to say many people and their children had enjoyed "a fabulous once-in-a-lifetime winter wonderland in central London".
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