Eurostar trains are cancelled today while the rail company tries to get to the bottom of problems which left thousands of passengers trapped in the Channel Tunnel for hours.
Wintry weather is thought to be to blame and today there were calls for the firm's chief executive Richard Brown to resign and admit Eurostar was "not adequately prepared".
The closure of the tunnel left thousands more people stranded in Kent and France as they waited to board trains, while the closure of Calais port added to the chaos.
Roads leading to Dover and Folkestone became blocked with traffic and there were reports that some families with young children had been trapped in their cars for more than 15 hours.
A Eurostar spokesman said test trains will run today before any passengers are allowed to board as the company tries to prevent a repeat of yesterday's chaotic scenes.
London St Pancras was packed as exhausted passengers arrived hours later than expected and hundreds more waited anxiously for news.
Nirj Deva, Conservative MEP for the South East of England, called on Mr Brown to resign as a result of "Eurostar's astonishing incompetence".
All affected passengers will be offered a full refund, £150 compensation and a free return ticket but Mr Deva described the offer as "paltry" and said it showed "how out of touch the management of this company really is".
"I therefore call on Richard Brown to admit that his company was not adequately prepared to deal with the situation today, and to do the decent thing and resign," he added.
Some scheduled passengers stranded at St Pancras planned to stay the night in the hope of some good news this morning while others said they would try again tomorrow.
Angelique Stastny, 21, said: "I would fly but I have too much luggage so I will get a train to Paris eventually."
A series of special trains had been planned last night to transport some of those delayed by the chaos but only one - destined for Paris - left.
A Eurostar spokeswoman later said the other services were cancelled because of adverse weather conditions.
"We have tried to run services but it's not possible," she said.
Another special service from Paris to London broke down after it came out of the Channel Tunnel, although passengers were eventually taken to London after long delays.
Mr Brown visited St Pancras yesterday as people arrived who had been trapped on four trains which broke down in the tunnel on Friday night.
He said he was "very, very sorry" about the inconvenience.
Many passengers said they were left without food, drink or power while in the tunnel.
Alison Sturgeon, from Ascot, left Disneyland Paris shortly after 7.30pm on Friday and arrived in London at 11am yesterday.
She said train staff had done a "dreadful job".
"They were useless at giving us information. There was no communication at all," she said.
There was also criticism of Kent Police after families were stuck on a gridlocked M20.
Roy Konarski said his Czech sister-in-law Rony Kovora was stuck near junction 12 for more than 16 hours yesterday with her daughters Amelie, four, and Phoebe, three.
"It makes you embarrassed to be English," he said.
"I think it's disgusting that nothing's been done.
"I phoned Kent Police and they said they were doing everything they can."
A spokesman for Kent Police said officers were doing their best to help those caught up in the disruption.
Freight traffic is being turned around in an effort to allow the backlog of tourist traffic to pass through the county, he added.
Chief Superintendent Matthew Nix said the welfare of motorists was his "primary concern".
Snow and ice also caused continued disruption to flights yesterday and wintry weather is expected to cause more delays and cancellations today.
Michael Dukes, forecast manager for MeteoGroup UK, the weather arm of the Press Association, said overnight temperatures between -2C (28F) and -7C (19F) were expected to cause widespread problems with ice and snow.
He said northern England and Wales are expected to be worst hit, but snowfalls could also reach 10cms in East Anglia.
Kent Police said queues on the M20 had eased by 4am today after freight traffic on the A20 at Dover was turned around as part of Operation Stack, allowing tourist traffic to pass to the ports.
As a result the backlog was cleared back to the Aycliffe roundabout, a spokeswoman said.
Eurotunnel and Port of Dover are operating normally now, she said, but tourists are being prioritised above freight.
The French authorities have indicated that freight will not be allowed to enter the country until late today, she added.
Kent Police Assistant Chief Constable Andy Adams said: "There is now some snow on the M20 and we are working with Highways to grit the road so that we can continue with the progress already made to clear the backlog of vehicles.
"We expect further delays to motorists this morning using the M20 and would therefore reiterate the need to travel only if necessary and, if so, to drive prepared with warm clothing and food.
"Due to further snow moving across the county, several roads are being closed at this time until they are gritted and safe to pass."
The A229 and A249 are closed in both directions.
Police said the M2 is "passable with care" in lane one but lanes two and three are closed.
The A21 is said to be "passable with care" at Sevenoaks.
Police said there is a lorry stuck on Quarry Hill in Tonbridge.
Kent Police said lorry drivers not yet in the county were advised to park outside the border and listen to news bulletins for information.
A spokesman said all major routes in the county were passable by 6am except sections of the M20 and the A20.
Superintendent Andy Rabey from Kent Police said: "Overnight we've been working very hard with our partners to clear the queues and help people get away for Christmas.
"Clearly there are still delays and we thank those waiting for their patience.
"If you have a crossing booked and haven't set out yet check with your operator before leaving home."
Overnight more than 3,500 cars crossed the Channel on ferries, a Kent Police spokesman said.
He added that the A20 remained very busy from junction 8 of the M20 (Leeds Castle) down as far as Dover.
Mr Brown responded to the call for his resignation by saying the most important thing was to learn lessons from the current problems.
"What's important at the moment is to get the service back and to really understand what happened and learn the lessons. That's what I will be doing and focusing on in the next few days," he told BBC News.
He said he was not "pretending" things had gone well but said things had not gone as badly as some people had claimed.
Mr Brown said refunds would be offered to ticket holders who did not want to take the risk of travelling on Eurostar this week.
He admitted he could not guarantee the service would be working but said: "We will not start services again until we're sure that we can get them through safely."
Eurostar is asking people not to travel unless they have to when services resume as it will be very busy.
Mr Brown said: "We are not going to be able to carry everybody who has booked yesterday and today."
He said the offer of a refund will stand until the backlog has been cleared, which he said would not happen before Christmas.
Kent Police later clarified the position relating to services running through the Channel Tunnel today.
Chief Superintendent Matthew Nix said: "Eurostar is not operating its passenger services at the moment, however Eurotunnel is operating its shuttle service.
"Eurotunnel has advised us that waiting times are up to two hours at the terminal. There is no space available for customers without reservations."
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