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A person has died after being hit by a train, while another is seriously injured following a separate collision on the tracks.
Emergency services were called to Staplehurst and Ashford this morning.
BTP officers were called to a line in Ashford at around 5.30am to a casualty on the tracks.
Paramedics attended and a man was taken to a local hospital with life-threatening injuries.
The air ambulance was also called.
A BTP spokesman confirmed this incident is not being treated as suspicious.
Trains were running at a reduced speed as a precaution to allow emergency services to deal with the incident safely.
Power was turned off but restored at around 8am and trains are now running on the route but delays continue.
BTP officers were also called to a line near Staplehurst railway station at around 7am to reports a person had been hit on the tracks.
Paramedics attended but the person was pronounced dead on the scene.
A BTP spokesman added: "This incident is not being treated as suspicious and a file will be prepared for the coroner."
At around 7.20am Southeastern tweeted: "We have just had reports of a person being hit by a train between Paddock Wood and Ashford.
"No trains can run on the between those stations. Disruption is expected until at least 10:00."
Southeastern confirmed buses will replace trains on the Paddock Wood to Ashford route.
Network Rail have said some passengers are still on the trapped train at Staplehurst.
The company told those stuck with the power off the train would have to be moved under its own power but due to an air leak, which engineers are trying to fix, that is not currently possible.
Tickets will be accepted on High Speed services between Ashford and St Pancras as well as London Underground via reasonable routes.
A Network Rail spokesman added: "Please be aware we have major disruption across’s Kent routes owing to emergency services attending incidents at Staplehurst and Ashford."