Eurostar has told passengers only to travel from Paris to London "if absolutely necessary".
Its services have been hit by delays with long queues due to industrial action by French customs officers.
Four trains were cancelled on Sunday. The firm has also cancelled three trains on Monday, two on Tuesday and three on Wednesday.
The company says tickets can be changed free of charge, or affected passengers can claim refunds.
"We recommend not to travel unless absolutely necessary, " Eurostar advised passengers on its website.
"All Eurostar trains are experiencing delays and long queues for journeys from Paris Nord due to industrial action by French customs until March 19th.
"These delays impact our planned timetables and cause subsequent cancellations," the firm said.
Customs officers are demanding higher pay and better working conditions.
They also want more staff which they say will be needed after Brexit, to help process British citizens who will no longer have European Union passports.
The industrial action is due to last until 19 March.
Passengers have been complaining on social media of long queues in Paris.
Catherine Hope tweeted that it had taken her four-and-a-half hours to clear all the queues.
Got to Gare du Nord 12.30pm to catch 5.07pm. Took 4.5 hours to clear all queues and caught the 4.50pm. It’ll be about an hour faster if you have an EU / UK passport (ironic 😉). Suggest getting there as soon as you can, it’s first come first serve. #eurostardelays #eurostar— Catherine Hope (@cath_hope) March 17, 2019
Another passenger said they had waited for four hours.
Hello @Eurostar Thanks for the email about compensation. Not sure how you work out a 78 minute delay? I arrived at Gare du Nord at 16.20 & left on a 20.45 service, having stood in a queue for 4 hours. I was booked on the 18.07 (after you cancelled the 19.07 the week before)? 🤔— Janina Heron (@VoiceoverJ) March 17, 2019
Eurostar says the delays are averaging at two hours and they expect similar delays on Monday.
Last week, French unions representing around 17,000 customs workers rejected a government offer of a €14m pay boost, saying it was not enough.
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