Two adult women, and two children – believed to an infant boy and girl – were pronounced dead at the scene.
The deceased are all believed to have been related to each other.
Detective Chief Superintendent Trevor Lawry, head of policing for Bexley, Lewisham and Greenwich said: “Our thoughts are with the family of the deceased, who have suffered such an awful and devastating loss. We have officers in the location and I know these sentiments are shared by residents across Bexley and London as a whole.
“Our inquiries are ongoing and we will continue to work with our colleagues in the London Fire Brigade to fully understand the cause of this terrible incident. In these very early stages we don’t believe the cause of the fire is suspicious.”