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
Two police officers helping to guard diplomats have been sacked for sharing pornographic images on their mobile phones.
A 32-year old man from Hampton has been jailed for five years historic sexual assaults in the late 1990s.
A teenager who was mistakenly released from prison after he was arrested on suspicion of attempted murder has been detained by police.