"They were the most vulnerable people, who needed to get back home to France and Belgium."
No arrangements were in place for Britons stuck in France, she added.
Lauren Copping, from Hoddesdon, Hertfordshire, said her three-year-old son Joshua was stranded in France after going to Disneyland Paris with his father.
She told BBC News: "Eurostar staff have been not very helpful at all.
"They went down to the check-in desk and they just shrugged their shoulders at them.
"I spoke to my son this morning. He is crying and wants to come home and we just can't get him home."
Ferry operator P&O is transporting a fleet of coaches across the Channel and on to Paris and Brussels to help people stranded by the cancellation of Eurostar services.
Spokesman Chris Laming said: "To avoid them having to spend a night at terminals in either Calais or Dover, we're putting on these coaches to enable them to get across the Channel."
Meanwhile, severe weather warnings remain in place in northern parts of the UK and freezing conditions have continued to disrupt travel.
Snow fell in Northern Ireland, western Scotland and north-western parts of England, and temperatures are expected to remain below freezing.
Ambulance services have urged people to take extra care walking and driving and to wrap up warm.
Clearly, if you're on a train stranded in a tunnel, it is a distressing experience
Richard Brown Eurostar chief executive
At Bristol International Airport hundreds of people were stranded when Easyjet scrapped five flights.
Flights were grounded for 90 minutes at Manchester Airport on Sunday morning as staff moved snow and de-iced a runway.
There have been delays at Belfast International Airport after it closed but later reopened, and Inverness Airport has also been disrupted.
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."
'Out of touch'
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."
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.
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.
This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.