The man, in his 20s, was pronounced dead at Fairfax House in Livesey Close, Kingston, at 08:00 GMT. His death is being treated as unexplained.
London Ambulance Service was initially called to reports of a injured man at the scene.
Nearby homes have been evacuated as a "precautionary measure", the Met Police said.
A man has been found dead at a block of flats where a "possible noxious gas" was detected.