Eurostar has told passengers due to travel from Paris to London to do so only if “absolutely necessary”.
Ongoing industrial action by French customs officers forced Eurostar to cancel four trains on Sunday (March 17).
It has pre-emptively cancelled another eight trains between Monday and Wednesday (March 18-20).
On Monday, the 7.04am and 8.37am Paris Gare du Nord to St Pancras trains were cancelled, and the 9.03pm Paris to Ebbsfleet International and St Pancras service.
The same 7.04am and 9.03pm services have been cancelled on Tuesday, and the 7.04am, 8.37am and 9.03pm on Wednesday.
Passengers can change their tickets free of charge for a different date and/or departure time, or claim a full refund.
“We recommend not to travel unless absolutely necessary,” said Eurostar in a statement.
“All Eurostar trains are experiencing delays and long queues for journeys from Paris Nord due to industrial action by French customs until March 20.
"These delays impact our planned timetables and cause subsequent cancellations.”
Eurostar chief executive Mike Cooper earlier this month said the operator would maintain the same level of service on its existing timetables in spite of Brexit.
Passengers in recent weeks have reported delays of upwards of two hours due to the ongoing industrial action in France.
French customs officers are in dispute over pay and conditions, and say more staff will be required post-Brexit to handle additional border checks.
Union officials last week rejected a new pay offer from the French government.
Eurostar says delays on Sunday were about two hours, and that it expects similar levels of delay this week.
It comes amid Eurostar’s early decision to trim its timetable through to the end of March for “operational reasons”.
On top of the new cancellations, Monday’s 7.31am and 7.01pm trains from St Pancras to Paris have been cancelled, as has the 7.07pm Paris to St Pancras service.
A further three trains have been cancelled a day Tuesday to Friday, one on Saturday, two on Sunday, and three more a day the week beginning March 25.