Four fire engines and around 25 firefighters tackled a fire at a flat above a shop on Lee High Road in Lewisham.
A balcony was destroyed by fire and part of a third floor flat was damaged by fire.
The Brigade's 999 Control centre received 17 calls alerting them to the fire.
The fire is believed to have been accidental and caused by the unsafe disposal of smoking materials.
A London Fire Brigade spokesperson said: "We’d rather you didn’t smoke at all, but if you are a smoker, it’s absolutely vital you ensure your cigarette is completely out when you’ve finished smoking it.
“If you don’t, you risk causing a fire which could not only destroy your home, but also cost you your life.
"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 1603 and was under control by 1655. Fire crews from Greenwich, Deptford, New Cross and East Greenwich fire stations were in attendance.