The 17-storey tower caught fire just before 2pm on July 11 on Hillingdon Street in Walworth.
A plume of smoke could be seen across London, with pictures shared from as far as Brixton.
An investigation into the cause of the fire was launched after it destroyed a flat on the 10th floor and damaged a balcony on the floor above.
Three people were injured and one woman was taken to hospital.
The fire is believed by the fire service to have been started by accident, although further details of the cause have not been specified.
WATCH: Shocking video shows huge plumes of smoke billowing from south east London flat fire
The fire was described by Station Commander Tony Perks as “very visible”, with the Brigade receiving 70 reports.
Crews from Dowgate, Dockhead, Soho, Whitechapel and surrounding fire stations had the fire under control by 3pm.
A London Fire Brigade spokesperson said: “Ten fire engines and around 70 firefighters were called to a fire at a block of flats on Hillingdon Street in Walworth.
“A flat on the 10th floor of a 17-storey building was destroyed and part of the balcony of the flat above on the 11th floor was also damaged by fire.
“Three people were assessed on scene by London Ambulance Service crews and one woman was taken to hospital.
“The Brigade received the first of around 70 calls at 1355 and Control Officers mobilised crews from Dowgate, Dockhead, Soho, Whitechapel and surrounding fire stations to the scene.
“The fire was under control by 1454.
“The fire is believed to have been accidental.”
