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Eurostar and High Speed train services were suspended earlier because of electrical supply problems between St Pancras and Ebbsfleet and Ashford.
Services between St Pancras International and Ashford International were suspended at about 10.15am due to the outage.
The lack of power also saw Southeastern services between St Pancras and Ashford suspended but the train operator has said London Underground are accepting tickets for reasonable routes.
Passengers at Ashford or Ebbsfleet can use their High Speed tickets on local stopping trains into London.
Southeastern tweeted earlier about the situation and said it hoped power would be restored soon and advised travellers of alternative routes.
The train provider later said trains which were trapped because of the outage had now been moved, but lines remained suspended whilst further investigations are carried out.
However, one line has now been reopened on Eurostar and travellers are experiencing delays of up to an hour and some services have been cancelled on Eurostar between St Pancras International and Ashford International due to the problem.
A single train line was opened at about 3pm but some Eurostar services are now departing and arriving at St Pancras International.
Departure boards are showing trains are delayed up to an hour and passengers should check before they travel.
The High Speed service remains suspended on Southeastern between St Pancras International and Ashford International.
Passengers at Ashford or Ebbsfleet can still use their high Speed tickets on local stopping trains into the capital.
A spokesman for Southeastern said: “Because of a problem with the power supply that is affecting all trains on the High Speed 1 route, Southeastern’s High Speed services are severely reduced this evening.
"Network Rail’s engineers are hoping to fix the issue soon, but in the meantime we’re strongly advising all of our passengers that would normally use our High Speed services to use our mainline services from London Bridge, Cannon Street, Charing Cross or Victoria to Ashford and the Kent coast.
"Passengers who would normally use the High Speed route should expect delays and busy services, with queuing systems in place at stations.
Passengers can check and re-plan their journeys by clicking here, the Southeastern On Track app, or by clicking here, or by following our Twitter feed @Se_Railway.