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Trains were held at Ashford International Station after a man jumped down onto the tracks.
It is understood that the man has fled the scene towards Ashford, and police and British Transport Police are still searching for him.
An eyewitness said: "A man seemed to be having an argument with someone he was with.
"He was getting more and more aggressive and he then went and jumped on to the tracks.
"He was jumping over the live lines time and time again.
"Members of staff from Southeastern asked him several times to get back up onto the platform but he refused.
"He then made for the fence and climbed over it, and it seemed like he was headed in the general direction of the designer outlet."
It is understood that trains are now running again, having been held while power to the track was turned off to minimise any risk to life.
A spokesman for British Transport Police said: "We received a report of a man trespassing on the tracks at Ashford International at 1.19pm.
"Officers are currently on scene and are conducting a search of the area."