Two fire engines and around 10 firefighters were called to reports of smoke issuing from a maisonette in Moremead Road in Bellingham.
Firefighters investigated and found a small cooking fire that had burnt itself out before the Brigade arrived.
One woman was treated at the scene by London Ambulance Service crews. Sadly, she died the following day.
The Brigade was called at 2237 on March 19 and the incident was over for firefighters at 2302. Fire crews from Beckenham and Lewisham fire stations attended the scene.