Police were called to the track near Wellingborough, between Kettering and Bedford around 12.45pm today (August 12).
Officers and medics arrived, but a person was pronounced dead at the scene.
Enquiries are now ongoing into the circumstances leading to the death.
East Midlands Railway services between London St Pancras, Corby, Nottingham and Sheffield face “major disruption” until the end of the day.
Trains may be cancelled or severely delayed by up to 90 minutes.
A BTP spokesperson said: "Officers were called to the line near Wellingborough at around 12.45pm today (12 August) following reports of a casualty on the tracks.
"Paramedics also attended, however sadly a person was pronounced dead at the scene.
"Enquiries are ongoing into the circumstances leading up to their death."
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