Police were called just before 4pm on Thursday to reports of a disturbance at Raglan House in Elephant Road, above the Sainsbury's supermarket on New Kent Road.
Police and ambulance crews arrived at the scene and a woman was found with serious injuries.
Superintendent Rachael Walmsley of the Met’s Central South Command said: "My officers will be patrolling in the area as our specialist crime colleagues go about their enquiries – if you have concerns please don’t hesitate to approach them.
"My thoughts are with all those affected by this tragic incident."
Just before 8.45pm police were called to reports that a man had fallen from a height at New Change in the City of London.
Despite the efforts of members of the public and medics, the man, aged 31, was pronounced dead at the scene.
Police say that both the man and woman were known to each other.
Detective Inspector Mike Nolan of the Met’s Specialist Crime Command said: “We know that local people will be shocked by this incident, and while we are at the very early stages of our investigation, I would like to reassure the community that we don’t believe that any other persons are outstanding in connection with this tragic sequence of events.
“I am keen to hear from anyone who has information relating to this investigation who has not yet spoken with police, and I thank local residents for their patience and cooperation as my team go about their enquiries.”
Anyone with information should call police on 101 quoting 4548/6APR.
To remain anonymous call the independent charity Crimestoppers on 0800 555 111.