Freezing weather continues to disrupt London transport
Several train services have also been disrupted
Freezing temperatures are continuing to disrupt transport in and around London following record overnight lows.
Temperatures plummeted to -14C in Northolt, west London - the lowest in the city for 20 years.
Thousands of passengers remain stranded at Heathrow Airport and people are asked not to come to terminals 1 and 3 due to congestion there. London City Airport runway has also been closed.
Eurostar customers were queuing since midday at St Pancras station.
Later it was announced that everyone who had queued had obtained a place on a Eurostar train to Europe.
Transport Secretary Philip Hammond said in order to clear the backlog at Heathrow Airport, night-flight restrictions would be lifted for the next four days.
Many mainline train routes from London also remain disrupted and the weather also affected some Tube lines earlier.Huge backlog
Eurostar is facing severe delays and cancellations due to speed restrictions in England and France.
St John Ambulance has sent a crew of eight as a precaution as hundreds queued in the cold.
Ann Cable, commissioner of St John Ambulance, 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.
"We'll be assessing anyone who needs our help to see if they need first aid and will be liaising with the London Ambulance Service to ensure that those who need emergency treatment are seen swiftly."
Eurostar said anyone due to travel on Monday who was not already at the station would not be able to get on their train.
It said it was not accepting bookings until Christmas Eve and would run a contingency timetable for several days.
Customers who have booked travel before Christmas are being offered a refund or an exchange of their tickets free of charge.
Airport operator BAA has issued an urgent appeal for travellers not to go to Heathrow unless their flights are confirmed.
A spokesman said Heathrow's second runway would not be open on Tuesday. He added there was a huge backlog of flights and the terminals had more people inside than they could safely deal with.
Passengers at the airport have also been offered free travel on the Heathrow Express back to Paddington.
BAA chief executive Colin Matthews said: "Heathrow was coping really well up until the middle of Saturday.
"The thing we underestimated was how much time it was going to take to clear snow underneath every single aircraft on its stand. We had to pick up literally 30 tonnes of snow underneath every aircraft before it could push back."
He urged airlines to announce cancellations earlier and to operate a "realistic" schedule to prevent overcrowding at the terminals.
Mr Hammond said flights carrying UK nationals who have been stranded abroad will also be allowed to land through the night.
"There is still a large amount to be done to restore Heathrow to full capacity and further snow and severe icing is anticipated over the next few days," he told parliament.
Mr Hammond said an inquiry would be held into the way passengers were treated at Heathrow Airport over the weekend.
Thousands of people were stranded as all flights were cancelled on Saturday and only a handful operated on Sunday.
A BAA spokesman said hundreds of extra staff were drafted in over the weekend and passengers had been put up in hotels.More snow expected
He said: "We are obviously not going to sit here and claim that it has gone well because it has been a very troubling time for many and we are extremely sorry for the disruption to people's journeys."
Staff at the west London airport are continuing to clear large amounts of snow and ice from the airfield and operations would be "significantly reduced" for several days, a British Airways (BA) spokesman said.
London City Airport has now cancelled all departures and arrivals.
A statement on its website said: "Due to severe weather conditions at London City Airport, our runway is presently closed.
"Due to the increase in customer traffic the airport is only able to accommodate passengers with tickets. Please do not attend the airport if you do not already have a ticket."
Several trains into King's Cross railway station have been cancelled because of overhead wire problems.
South West Trains has suspended services on some routes and is operating a reduced timetable on others.
There is also severe disruption on most First Capital Connect routes.
On London Underground's Metropolitan Line, which extends as far as Chesham and Amersham in Buckinghamshire, there were severe delays due to snow.
London Ambulance Service said it had been its busiest period on record.
Staff took more than 17,000 calls from between when the snow started to fall on Friday, until Sunday night - an increase of 30% compared to an average weekend.
Forecasters have predicted a dry day with temperatures struggling to get above freezing. More snow is expected in south-west London this evening.