LeShuttle - which carries road vehicles and passengers through the tunnel - is also warning of delays. A broken down LeShuttle train has now been removed, but the operator says services "remain severely disrupted"
One family in Calais are stuck in their car on LeShuttle with three young children - while a couple travelling from the Netherlands to a wedding in Maidstone say they might just arrive in time for "dessert and cheese"
The company, Eurostar" that operates the Channel Tunnel says train traffic will "gradually resume" this afternoon. Eurostar says some of its services will also resume, but it still strongly advises passengers to postpone their journeys to a different date.
If the disruption impacts you, here's what Eurostar is advising:
Exchange your booking for free to travel in the same travel class but at a different time or date
Cancel your booking and claim an e-voucher - you'll have 12 months from the date of your disrupted journey to redeem it on Eurostar's website
Cancel your booking and get a refund - this will be for the ticket value, but won't include any booking fees
Eurostar says passengers will have three months from the date of the ticket to claim their preferred option.
Two American tourists have spent hundreds of pounds to reach Paris tomorrow after their Eurostar service was cancelled today.
Haley Adams, 38, and Hannah Hagar, 35, paid $580 (£430) for flights to the French capital to celebrate Hagar's 36th birthday there.
The pair have had their Eurostar tickets refunded but say they will have to pay for an extra night at a hotel in London and cannot get a refund from the hotel they were going to stay at in Paris tonight.
Haley and Hannah, who are from Austin in Texas, arrived at St Pancras at 08:00.
They had reached passport control when they discovered their train had been cancelled. "There’s been a lot of queuing," says Haley. "We have been here for five hours."
A family from Mexico say their trip of a lifetime has been cast into doubt as their Eurostar service was cancelled.
Monserrat Hernandes, her brother John Paul and mother Olga are among dozens of people looking frantically at their phones near the Eurostar departure area at St Pancras International.
The family got on the Eurostar just after 08:00 GMT but after their train left for Paris it had to return due to the incident. “The train stopped and we were in Camden or somewhere like that,” explains Monserrat. “That’s what maps on my phone showed.”
“They say nothing is travelling today… there’s no hope for leaving tomorrow.”
The family spent Christmas in London and are due to spend New Year's Eve in Paris before travelling on to Rome and Madrid. They are now searching for a flight or a ferry to make it to Paris.
“It’s like an American movie,” adds Monserrat. “Hopefully I find the love of my life.”
Betty Ndukaeze has been trying to travel to Paris to celebrate New Year’s Eve with eight of her family.
Her brother Charles, his wife and three children have been visiting London from Nigeria.
The family say they were left trapped on a Eurostar train for over four hours - and it then had to return to St Pancras due to the disruption.
The group first arrived at St Pancras shortly after 05:00 GMT to catch the 07:01 GMT Eurostar service. But the train did not leave until around an hour later and was then forced to turn back.
"It was chaos from the moment we got here," says Betty. "They kept announcing there was a problem with the train ahead of us and saying they were trying to fix the problem.
"We just got back here. The journey back from where we were stuck was only 20 minutes.
The family are now worried they may have to spend "a fortune" to stay in a hotel near St Pancras, as they try to get another train later in the week.