Eight fire engines and around 60 firefighters tackled a fire at a shop with dwellings above on High Street in East Ham.
Part of a first floor flat, second floor flat and roof were damaged by fire. Thirty-three people left the building before firefighters arrived and there were no reports of any injuries.
The fire is believed to have been caused by the unsafe use of incense sticks.
A London Fire Brigade spokesperson said: "Incense sticks, candles and oil burners are one of the most common causes of fire within homes. It’s really important that you never leave these items unattended.
"Make sure you place incense sticks in a suitable, fire-resistant holder and keep them away from curtains and anything else that can easily catch fire. Remember to put them out entirely when you leave the room and especially before bed.
"We also recommend taking some time to carry out a few simple checks to keep yourself and your loved ones safe. The Brigade’s online Home Fire Safety Checker can guide you around your home and provide you with specific advice to reduce fire risks.”
Control Officers took the first of five calls regarding the fire at 2015 and the fire was under control by 2258. Crews from East Ham, Brixton, Poplar and surrounding fire stations attended the scene. One of the Brigade's 32-metre turntable ladders was used at the scene as an observation tower to help fight the fire from above.