Eurostar passenger Claire McKinney Williams, who is 35 weeks pregnant and unable to fly, was stranded at a hotel in Brussels.
She told the BBC: "It's been very disruptive. We haven't had any help, we've been over to Eurostar in the station, and they've not been very helpful, they haven't given us any help on alternative ways home or anything."
Eurostar has not said when services will be back up and running, with a message on its website simply saying: "We are committed to restoring our services as soon as possible but our key priority is the safety and comfort of our customers."
Eurostar chief executive Richard Brown asked people not to travel unless it was essential.
He said: "When we resume service it's going to be very busy, we're not going to be able to carry everyone who's booked yesterday, today and during this week."
'Out of touch'
Passengers who have suffered delays will be offered a full refund, £150 compensation and a free return ticket.
The compensation would be offered until the backlog of passengers was cleared and the service was back to normal - which Mr Brown did not expect to happen before Christmas.
I'm not saying it went well, I'm saying it went rather better than actually a lot of people say
Richard Brown Eurostar chief executive
Nirj Deva, Conservative MEP for the South East of England, said he wanted the Eurostar chief executive to step down.
The company had not been adequately prepared for the situation, and Mr Brown should therefore "do the decent thing" and resign, he said.
Mr Brown told BBC Breakfast he was "very, very sorry" for the inconvenience and described events as "unprecedented".
He admitted it had taken a "very long time" to evacuate people from the trains.
"Clearly, if you're on a train stranded in a tunnel, it is a distressing experience," he said.
He conceded it took too long to get trains out to people and said while trains had spare water, it ran out.
Shadow transport secretary Theresa Villiers said the disruption was a "catastrophe" for people trapped trying to get home for Christmas.
She said: "After a reprieve from BA strikes, it is a huge concern to see travellers hit so hard by this crisis."
On Sunday, all ferry services from Dover to Dunkirk, Boulogne and Calais were running, and traffic queues had eased.
The Port of Dover said traffic was running freely on the A2 and A20 into Dover, and freight traffic stuck on the M20 was being called forward in batches to be shipped across the Channel.
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