All Eurotunnel services have been “temporarily suspended” due to “unexpected strikes” by French staff.
An update on the company’s website said: “Due to industrial action in France, all Le Shuttle services [which carry vehicles and passengers] have been temporarily suspended.
“We apologise for the delay to your journey. Further updates will be provided shortly.”
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The disruption is affecting journeys to and from London, threatening Christmas plans for many travellers.
The industrial action is reported to be over end-of-year bonus pay.
Getlink, the company that manages and operates the infrastructure of the Channel Tunnel, said trade unions had rejected a €1,000 (£866) bonus proposed by management.
The union has demanded for the amount to be trebled.
Last few unaffected passengers arrive in Paris
Cancellations set to last until at least Thursday night
It is unknown precisely how long disruption is expected to last.
Greg Hands, minister for London, posted on X (formerly Twitter) he understands all trains from London to Paris have been cancelled until 7pm on Thursday evening.
Trains from Paris to London are cancelled until 8.30pm, Mr Hands added.
He said trains from London to Brussels are cancelled until 7.30pm, with only one train (6.51pm) running in the opposite direction from Brussels to London.
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Some services turned around
Eurostar (which carries passengers on foot) said in a post on X: “We would recommend postponing your journey if you can, even if it’s until tomorrow.”
Some services that had already departed were stopped on route and returned to their starting point, it added.
Le Shuttle said in an update: “Due to industrial action our service is suspended. Customers are advised that, as a consequence of this incident, access to our site is currently unavailable.
“If you are due to travel today please make alternative arrangements or modify your booking.”
Unverified posts on social media showed people stuck on trains or in stations as they tried to reach London or Paris.
There is currently no information on services planned for tomorrow, Eurostar said.
Sky News has contacted Getlink for comment.