Police said the body is being held for possible repatriation in case the man's identity is established.
Mortlake residents and business people speak of a similar death in recent years, but disagree about the timing and the details.
"People say the same thing happened a few years ago a few blocks away" said Jay Sivapalan, 29, who works at the Variety Box convenience store half a block from where the body landed. "We are near Heathrow and when they lower the landing gear, the body falls out."
Others believe the incident may have happened 10 years ago. Police said they had no information about other stowaway deaths.