Thousands of people face further disruption to their Christmas travel plans as cold weather continues to grip much of the country.
BA cancelled all short-haul flights out of Heathrow while Eurostar passengers in London queued around the block.
Gatwick Airport is shut and will not reopen until 0600 GMT on Tuesday.
BAA has apologised for spoiling so many people's Christmases and the Met Office has warned of more snow and ice in parts of the UK overnight.
Heathrow airport officials said no more than a third of all flights would operate until 0600 GMT on Wednesday and warned passengers to expect delays and cancellations, possibly until Christmas Day.
Overcrowding was so bad in some areas that passengers with flights scheduled to depart from terminals 1 or 3 on Monday were told not to travel to the airport.
BAA said the south runway would remain closed on Tuesday and advised people not to travel to the airport unless their airline had confirmed the booking.
Transport Secretary Philip Hammond said aviation was a "safety-first business".
And in a statement to MPs, Mr Hammond said rules on night flights would be relaxed for the next four days to help deal with the backlog.
This would mean allowing incoming flights to arrive through the night, while outbound planes could take off until 0100 GMT, he said.
In other delays:
- At Gatwick, 600 flights took off and landed at the airport on Monday, but the airport shut about 2000 GMT on Monday amid fresh snow
- Cardiff Airport, closed for most of the day, reopened at 2030 GMT but warned of flight delays and cancellations
- Edinburgh, Aberdeen, Glasgow, Birmingham, Luton, London City, Bristol and Southampton airports all said flights would be subject to delays and cancellations
- Exeter closed a runway on Monday, but said it hoped departures on Tuesday would run as scheduled.
- Stansted is said to be operating as normal.
- Elsewhere in Europe, airports in Frankfurt, Paris, Florence and Amsterdam were severely disrupted.
There was also disruption to road and rail travel on Monday:
- By Monday evening, problems on the UK's motorways seemed to be easing but BBC Travel was reporting severe disruption on the M25 in Surrey and the M58 in Merseyside
- Some London-Leeds and London-York services were cancelled on the East Coast Main Line
- No trains were running between Birmingham New Street and Coventry
- The AA said it expected to attend about 28,000 call-outs nationally on Monday, compared with 10,500 on a normal Monday
Martine Gurbhoo is at Gatwick Airport, having supposed to have flown to Paphos on 19 December.
She told the BBC she and her husband had moved to the ticket hall "as we have been told to get out of the main departure lounge, otherwise we will get escorted by the police".
And Damian McCarthy of Harpenden had to return home after spending most of the day at Gatwick with a five-year-old child.
He said other passengers were "very angry, with many refusing to leave the terminal building."
People at St Pancras station queued for up to eight hours for Eurostar services to the continent, which was also suffering from severe weather. The station was so busy that many had to wait outside in the bitter cold, lined up around the terminal building.
St John Ambulance was asked to send eight crew members to the station as a precaution.
Ann Cable, commissioner of St John Ambulance in London, said: "Many have been standing out in the cold for several hours and it's understandable that Eurostar want to make sure they're properly looked after."
The BBC's Andy Moore said that, according to the station's manager, everyone who queued for a place on Monday got on a Eurostar train to Europe.
About 100 people are queuing overnight but they are passengers who are early for trains on Tuesday morning.
One worker at St Pancras estimated there were 3,500 people - most of them families - queuing outside the station in the mid-afternoon.
A Salvation Army tea truck was serving hot drinks, and spirits were surprisingly relaxed despite Eurostar staff "keeping out of public view," he told the BBC.
But BBC producer Nicki Stiastny, who queued for eight-and-a-half hours on her way to France, said police angered many when they stopped letting people join the end of the queue.
She said people were given "very limited information" and what had been passed on was "by word of mouth", leaving passengers "tired and frustrated".
BBC weather forecaster John Hammond said southern England bore the brunt of the snow on Monday, with 20cm falling in parts of Devon and Cornwall.
Through the evening, snow in southern parts of the UK will ease, say forecasters, although the far south-east might see some heavy snow for a time. More snow showers are expected along the northern coast.
Overnight, it will remain bitterly cold and Tuesday will start off very icy with temperatures well below freezing, say forecasters.
Parts of Scotland and Northern Ireland are likely to see the coldest temperatures overnight, dropping to -17C in Omagh.
Sub-zero temperatures will persist across almost the whole country on Tuesday.
The Foreign Office has updated its travel advice for France, warning of disruption to road, rail and air travel in the country.
Most schools in England have already closed for the Christmas break but 472 schools shut early on Monday in Northern Ireland, 170 in Wales and at least 50 in Scotland.
The bad weather also led to a sharp drop in weekend shoppers, with retail research group Synovate saying UK footfall was down nearly 25%, compared with last year.
The Highways Agency said it was doing its best to keep major roads in England clear, but advised motorists to check traffic and weather conditions before deciding whether to head out.