LONDON — Eurostar suspended all its rail links between London, Paris and Brussels on Sunday as cold weather caused chaos on the high-speed passenger line for a third day, with no relief in sight.

Richard Brown, chief executive of Eurostar, apologized in an interview with the BBC and said full service might not be restored before Christmas Day, which is Friday.

The problems began Friday when five Eurostar trains broke down in the tunnel under the English Channel. After reports that passengers on at least one were left without water, food or information, Nirj Deva, a Conservative member of the European Parliament, said Eurostar was guilty of incompetence.

“I therefore call on Richard Brown to admit that his company was not adequately prepared to deal with the situation and to do the decent thing and resign,” Mr. Deva said in comments released by his office.

Asked by the BBC if he would quit, Mr. Brown said it was important to get the service running again and to find out what had gone wrong. “That’s what I will be doing and focusing on over the next few days,” he said.

The company, which is owned jointly by a consortium of British, French and Belgian rail operators, attributed the problems to the difference in air temperature inside and outside the tunnel. It said excessive condensation had then produced a series of electrical faults.

The unusual temperatures on the French side of the tunnel were part of wintry weather that stretched across Europe, killing 15 people in Poland and leading to cancellations at airports in several countries, The Associated Press reported.

Eurostar said more than 2,000 people were trapped in the tunnel on Friday, sometimes for two to three hours, with delays to journeys as long as 18 hours. On Saturday, a train from Brussels to London made the journey successfully, but another from Paris broke down and was delayed severely.

The company said it would offer travelers who suffered major delays £150, or about $240, as compensation in addition to a refund on their tickets and a free return ticket. It also offered to pay “reasonable” out-of-pocket expenses.

Eurostar, which carries about 25,000 passengers a day, said it was completing test runs of trains without passengers to try to resolve the problems before making any statement on resumption of services.

“I can’t guarantee our service will be working because we have suspended the service today until we get to the bottom of what happened on Friday night,” Mr. Brown told the BBC. “We will not start services again until we’re sure we can get through safely.”

In Britain, The Daily Telegraph reported one family’s account of a journey, from Disneyland Paris to London, during which the electricity failed, passengers were plunged into darkness and the atmosphere became stifling because of the lack of air conditioning.

It quoted one traveler, David Gannon, as saying that his 7-year-old daughter panicked. “People around us were having panic attacks, so she got really flustered,” he said. “She was clinging to us the whole time.”

This reporter attempted the trip from Paris to London over the weekend. It took 10 hours, to be sure, but that should perhaps read “only” 10 hours, a result of seasonal kindnesses from total strangers that made the trek possible.

It began on Saturday, when the 5:13 p.m. Eurostar train from Paris boarded 30 minutes late before being canceled altogether. The backup plan was to take the high-speed train, the T.G.V., to Calais, then cross the Channel by ferry and head up to London.

So far, so good. The T.G.V. left the station only 10 minutes late on its trip of an hour and a half. But upon arrival shortly after 8:30 p.m. at the snowbound Calais rail station, there were no buses or taxis to get to the port from which cross-Channel ferries operate.

Voilà, the first kindness. A French couple, collecting their daughter who had traveled from Toulouse, went out of their way to offer a ride to the ferry terminal.

But luck again took a turn for the worse.

The ferry companies refused to sell tickets to passengers traveling without automobiles. Sea France said it was against the rules for all their ferries, and P&O said it could take foot passengers only during daylight hours. Despite the travel chaos, neither would make an exception.

And then a second gift appeared. A group of seven snowboarders returning from vacation, all in their early 20s, took pity, offering the remaining space in one of their two cars, which were already booked on the ferry to Dover.

For the price of a beer for the nondrivers and a small contribution toward the fuel, they drove many kilometers off their 20-hour route from Val d’Isère, in the French Alps, to Leeds, in northern England, and stopped in London at 2 a.m. on Sunday. They even played a CD of the Stranglers to make their middle-age passenger feel at home.

Others, not so lucky, were left stranded at Calais or in Paris.

Passengers hoping to travel on Sunday were left with a series of unenviable options when snowfalls forced delays and cancellations of some flights from Brussels, and there was heavy traffic congestion on the English side of the Channel after the delay on the separate Eurotunnel train link, which transports vehicles and which was still running.

Some people were taking no chances, like Chantal Hughes, an official at the European Commission in Brussels, who said she feared having to spend Christmas in Belgium rather than with her family in England. She told of paying a total of £500 on a variety of train and plane tickets, just to be safe.