thousands of travellers have been stranded at Heathrow airport overnight, and hundreds more at Gatwick, as snow continues to disrupt much of the UK. 
There will be no flight arrivals at Heathrow on Sunday and only a handful of departures, while many Gatwick flights are affected.
Problems persist at airports UK-wide, while the Met Office is warning of icy roads across much of England and Wales.
More heavy snow is expected in eastern Scotland and north-east England.
Up to 10cm of snow are expected in these areas, and up to 20cm in hilly areas.
Forecasters said the UK was hit by extremely low temperatures overnight, with most parts of the country struggling to get above minus 5C, while fresh snow fell in eastern Scotland and north-east England.
Hundreds of thousands of Britons had been due to fly this weekend, according to travel association Abta, which estimated that four million people expected to go abroad..
Heathrow airport told the BBC that "a few thousand spent the night in the terminals" but said just four short-haul and three long-haul flights would leave on Sunday morning. It hoped to be operational on Monday.
Sue Kerslake spent the night on a terminal floor with her three young grandchildren after their Cathay Pacific flight to Hong Kong was cancelled.
Having arrived at the airport at 0800 GMT on Saturday, they sat on a plane for seven hours before being told it was not taking off.
"There were thousands of people in departures overnight and it got quite intense at times. The bars were open and some people were drinking and got quite nasty," she said.
Stuart Gash, from Swindon, who had been due to fly to New York for a Caribbean cruise with his wife and two children, said UK airports seemed unable to cope at the first sign of snow.
'Miserable'
He said: "There was no more than two inches of snow and yet the runway is totally covered. Why aren't they ploughing it, why aren't they gritting it, why aren't they salting it?"
Andrew Teacher, from Heathrow operator BAA, said it had invested more than £6m in the last year in technology to move snow and de-ice runways and that staff had been working through the night.
But he said: "There comes a point where you cannot do any more; when you're moving snow and it's freezing behind," adding that many planes had been frozen into parking spaces.
He apologised for the "miserable" situation but said problems had been caused by "an extreme amount of snow in a very short space of time" and safety had to be prioritised.
"Overnight we had hundreds of people drafted in to focus on helping passengers who have remained in terminals. We've given them blankets, water and food and are trying to make people as comfortable as possible."
The Independent's travel editor Simon Calder said very few of the 400,000 passengers due to fly out of Heathrow this weekend would get to their destinations. At Gatwick, the BBC's Helen Fawkes said 90,000 people should fly out on Sunday but that there had already been 50 cancellations.
A Gatwick spokeswoman said it was doing everything it could to "get passengers on their way".
"Passengers must check with their airline before setting out for the airport to reduce congestion and avoid disappointment," she said.
Airports in Germany, France, Italy and the Netherlands are also suffering cancellations and delays.
Stansted, Luton, Exeter, London City, Aberdeen, Birmingham, Bristol and Southampton airports said flights would be subject to delays and cancellations throughout Sunday, while the runway at Jersey Airport was closed until at least 0915 GMT.
Infrastructure 'seized up'
Ryanair has cancelled 84 flights to or from UK airports, mainly in the London area.
In Northern Ireland freezing conditions continue to make travel difficult following some of the heaviest snowfall for 25 years - with more forecast.
Belfast International Airport has reopened, although knock-on effects have caused delays.
Monarch Airlines managing director Tim Jeans said reassessment of the UK's transport infrastructure was needed.
"We have not coped well. The infrastructure - not just at the airports but the road infrastructure - completely seized up. The M25 going towards Heathrow and Gatwick virtually impassable within an hour of the snow starting to fall."
On what is one of the busiest weekends of the year for travel and shopping, other problems caused by the weather include:
- The AA said it dealt with 16,000 calls on Saturday, compared with 9,000 on an average pre-Christmas Saturday
- There was some disruption to South West Trains and First Capital Connect services, although most other routes were now operating normally, according to National Rail Enquiries, which has provided a new passenger phone number - 08453 017 641
- Sunday's sporting schedule was again badly affected, after wide postponements of football, rugby union and horse racing fixtures on Saturday
- An urgent appeal is being made for blood donors, particularly those who are O negative, as stocks are running low
- Companies have warned of a backlog of deliveries which may not reach customers before Christmas
On Saturday, Jon Caudwell, from the Highways Agency, said they were doing their best to keep major roads in England clear but needed help from motorists who should "really seriously consider" whether they needed to go out.
He said he was surprised at the level of traffic on the roads, given the advice not to travel. He said in some areas abandoned vehicles and jack-knifed lorries had blocked access for gritters.
A Department for Transport spokesman said: "The weather over the last 24 hours has been exceptionally severe. Government continues to monitor all aspects of the situation."
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