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.
More top news
Rory Geoghegan claimed the lack of support he received from the Met shows how frontline officers are being taken for granted.
A registered sex offender who admitted grooming a 14-year-old girl and then sexually assaulting her has been jailed for over four years.
The chief executive of SECAMB ambulance service, which deliberately delayed 20,000 patient responses, has left 'to pursue other interests'.