BTP officers were called to Eltham rail station on Friday, 27 September following a report of a body in the car park.
BTP and Metropolitan Police officers attended the incident, which was reported to BTP at 10.30am and is currently being treated as non-suspicious.
Medics from London Ambulance Service also attended but the man was pronounced dead at the scene.
Enquiries are ongoing to establish the full circumstances surrounding the incident, including the minutes leading up to the man's death.
A file will be prepared for the Coroner.
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"All it takes is for somebody to see me - and I could just die, just like that. I could want to go to the shop and not come home."
Before the killing, Peters searched the internet for "serial killers", "treatment of child killers in prison" and "premeditated murder".
Arriva Rail North, Greater Anglia and South Western Railway are all affected.