Police were alerted to reports of a man acting aggressively at a bar on The Broadway in Hammersmith at 2.45am on Sunday.
It was reported the man had assaulted a number of people before escaping the scene.
Soon after, police found a man had fallen from a nearby building site.
The man was pronounced dead at just after 3am.
His family have been informed and a post-morterm will be carried out.
A spokesperson from the Metropolitan police said: “Police began a search of the area to track down the man.
“A short time later officers became aware of a 33-year-old man who had fallen from height on a nearby building site. They carried out emergency first aid until the arrival of paramedics.”
The statement added: “As is routine in these circumstances, the Met’s Directorate of Professional Standards and the Independent Office for Police Conduct has been informed. The Health and Safety Executive has also been made aware.”