Eurostar said only one train would leave London on Tuesday
Travellers heading to the continent face disruption from two separate strikes by workers in Belgium and France.
A 24-hour stoppage by Belgian rail workers, which was due to start on Monday, will halt London to Brussels services through the Channel Tunnel.
Eurostar said it would be able to run only one of its services from London.
A 36-hour stoppage by general workers in France, from Wednesday, is expected to affect pre-bank holiday travel.
Eurostar advised all travellers to and from Belgium on Tuesday that they should change their travel plans and exchange their tickets for alternative dates or obtain refunds from the point of sale.
It said that Brussels Midi station would be closed for the 24-hour strike.
There would be no high-speed onward rail connections from Brussels to destinations in France, the Netherlands and Germany.
The only train leaving London's St Pancras international would be the 19:34 BST service, on the assumption that the Belgian high-speed line would re-open at 21:00 BST.
The French strike is due to begin at 1900 BST on Wednesday and last until 0700 BST on Friday.
Although Eurostar services to Paris are expected to operate as normal during this French strike, there is likely to be severe disruption for travellers within France.