The body - believed to be that of a man - was found in Clapham just before 15:40 BST on Sunday.
The individual is believed to have fallen from a Kenya Airways flight from Nairobi, police said.
A neighbour said the man fell a metre away from a resident who had been sunbathing in the garden.
The man, who did not want to be named, said he heard a "whomp" so he looked out of an upstairs window and saw the body and "blood all over the walls of the garden".
"So I went outside, and it was just then the neighbour came out and he was very shaken," he said.