A post-mortem examination held at St George's Hospital mortuary failed to establish cause of death and the coroner ordered further tests.
The 29-year-old man has been discharged from hospital. He has not been arrested and has assisted officers as a significant witness.
A Metropolitan Police spokesperson said: "Detectives from Wandsworth borough investigated alongside the Port of London Authority and in consultation with the Marine Accident Investigation Branch. The incident is not believed to be suspicious.
"An inquest will open on Tuesday, December 15, under the Wandsworth Coroner."