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Trains were disrupted between Sheerness and Queenborough after thieves made off with about seven metres of cable.
Buses replaced services until about 4pm after the cables were stolen at some point overnight.
Southeastern first tweeted about the problems shortly after 5.30am this morning.
A statement on Southeastern's website said: "Due to a suspected cable theft, the electricity supply to the railway between Sheerness and Queenborough failed overnight."
It added the line had to be closed whilst Network Rail engineers worked to restore power to the area.
The damage meant trains on the Sheerness line could only run between Queenborough and Sittingbourne.
There were four replacement buses running between Sheerness and Queenborough in place of cancelled trains.
Network Rail apologised to customers for the disruption to their journeys.
A spokesman added: "Overnight we discovered around seven metres of cable had been stolen, which meant trains could not draw any power between Queenborough and Sheerness."
Engineers were able to replace the cable and complete the work by 4pm.
British Transport Police (BTP) said officers were called shortly after 3.10am to support Network Rail engineers.
A spokesman said: "It is believed, at this time, that the cause of the disruption is cable theft and officers have since launched an investigation.
"Anyone with information is asked to contact BTP by sending a text to 61016 or by calling 0800 40 50 40, quoting reference log 36 of August 29, 2018."
A similar theft took place in May, when signalling cables were stolen from railway lines near Queenborough.
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