The whole of a balcony and a small part of a third-floor flat was destroyed by fire.
The Brigade’s 999 Control Centre received 17 calls alerting them to the fire.
A London Fire Brigade spokesperson said: “Firefighters recommend that you have a look at our online Home Fire Safety Checker to make sure there are no hidden hazards in your home.
“The online tool will ask you a series of questions that will help us work out the level of risk in your home, or the home of someone you care for. It only takes a few minutes to get tailored advice to keep yourself and loved ones safe from fire.”
The Brigade was called at 4.03pm and was under control by 4.55pm Fire crews from Greenwich, Deptford, New Cross and East Greenwich fire stations were in attendance.
The cause of the fire is under investigation.
