Eurostar, the high-speed train service connecting Britain and continental Europe, said all of its trains to and from London were canceled until further notice after a major power failure inside the Channel Tunnel, disrupting plans for thousands of people during one of the busiest travel weeks of the year.

The disruption, caused by a fault in the overhead power supply and the subsequent breakdown of a train within the 31-mile tunnel, left passengers stranded for hours.

“We advise our customers to rebook their journey for another day, with free exchanges available,” Eurostar said in a statement, urging passengers not to go to affected train stations.

By early afternoon, the train that had broken down — part of a service known as LeShuttle that transports vehicles under the English Channel — had been moved out of the tunnel, and trains were headed back to the cities from which they had departed. The Eurostar terminal in London St. Pancras International station was jammed with passengers trying to rearrange their plans.

Nearly 20 million people last year traveled on Eurostar, which runs trains between London and Paris and also serves Brussels, Amsterdam and a few other cities in northern Europe.

Jylian Repetski, an American who was traveling in Europe over the winter holidays, said she had been stuck on a train heading to Brussels from London for more than five hours. The train, which had been scheduled to leave London just after 7 a.m., departed an hour late and then was stopped in England outside the Channel Tunnel for about four hours, before returning to London around 12:30 p.m., she said.

Ms. Repetski, a director at a technology company who lives outside Philadelphia, said she, her husband, two children, her ex-husband and his wife had planned to spend the day in Belgium sightseeing, enjoying the architecture and sampling Belgian chocolate. It was “definitely a sad waste of five hours during a short trip,” she said.

At St. Pancras International, throngs of people stood in the main hallway on Tuesday afternoon, scrolling Airbnb or trying to find ways to get to France by ferry or plane.

Stephanie Letessier, 43, had been trying to get home to the Paris area, but once she found out her train was canceled she quickly arranged to stay with friends in London until Friday. “I was just supposed to go back to have a quiet New Year’s Eve in France,” said Ms. Letessier, who works at an A.I. start-up.

Laurence Duhamel and her mother, Roseline Edouard, had just fulfilled a lifelong dream by visiting London and needed to get back to Paris for a medical appointment and New Year’s Eve plans on Wednesday.

They found out about the disruption when they arrived at the station, Ms. Duhamel said. She said that she and her mother had booked flights to Geneva, where they would spend the night before taking a train to Paris in the morning. In all, she expected the disruption would cost about 800 euros (about $940).

“We have that money,” Ms. Duhamel said. “But we just didn’t want to spend it like this.”

Paris’s Gare du Nord station was also crowded with travelers trying to make alternate arrangements.

Charles Gobert, a Canadian who had plans to travel to London from Paris, said that the train he had boarded that morning turned around after reaching Lille in northern France. “We can’t even take a train tomorrow because all the trains are full,” said Mr. Gobert, 69. “It’s a big disappointment.”