Some passengers were delayed by up to nine hours and Eurostar has cancelled a number of trains scheduled for Tuesday.
It said a sagging overhead cable meant trains had to be switched from high-speed lines to slower ones, adding it was “very sorry for any inconvenience”.
Police boarded one train, although the purpose of their presence was unclear.
The journey between London and Paris usually takes about 2 hours and 15 minutes.
Eurostar later said all delayed trains heading for St. Pancras station in London had arrived.
Eurostar expects to run a normal service from lunchtime.
The company told passengers with tickets for cancelled trains to exchange them for another day if possible.
It said passengers booked on the 09:12 GMT service from London could travel either on the 07:54, 08:31, or 10:24 services.
Those booked on the service leaving Ebbsfleet at 09:31 and Ashford at 09:55 could join a later train departing those stations at 10:42 and 11:00 respectively, it added.
Kandy Woodfield, from London, was on a train that left the city at 14:01 GMT but she was still on the train seven hours later.
“It has been hellish. We have not been kept informed,” she said.
“They eventually gave us free water but that is it. The bar has made an absolute killing. I think it is terrible. There are elderly people and young children on board.
“I saw at least six policemen get on the train, I don’t know if there has been any trouble but they keep walking up and down the train.”
Similarly, Therese Kelly, from London, who was stuck for eight hours, said: “We had no announcements about why the train was so delayed or why it kept stopping, the train didn’t move for hours.
“At one point policemen started walking through our carriage of the train, they wouldn’t speak to us and I thought ‘Oh God, are we in the middle of some security breach?’ I was really scared. The whole train journey was brutal, totally brutal.”
Six hours after leaving Paris Debbie Goodier, from Croydon, south London, had only reached Calais.
She had travelled to Paris for a day trip to celebrate her wedding anniversary.
“We were delayed two hours on the way out and now stationary on the way back. Not for the first time,” she said.
Ryan Armstrong, who was travelling to Amsterdam via London, missed his connecting flight because of the delays.
“We were basically on the train for nine hours. We hardly moved; there was a lot of standing still. At one point the power was cut so we couldn’t see anything or get any information,” said the London man, who added that the staff on his train had been “helpful and supportive”.
She said four train services had been cancelled on Tuesday morning to “regulate” the service.
“We are trying to do everything we can to get passengers to their destination. We are doing everything we can to make their journey as comfortable as possible,” she said.
On its website, Eurostar stated: “Due an overhead power cable on the line the services below will be cancelled on Tuesday 6th March.
“If you are booked to travel on one of these services, we recommend that you exchange your ticket for travel on another date as other services may also be subject to delay. You can do so for free at any time in the next two months by calling our contact centre on 08432 186 186.”
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