Part of a three-roomed flat on the third floor of the building was damaged by fire. Nine people left the building before the Brigade arrived. There were no reports of any injuries.
Firefighters used a turntable ladder as an observation platform and used a thermal imaging camera to check for fire spread.
The fire is believed to have been accidental and caused by sunlight refracted through a glass bottle, which ignited cardboard packaging on the kitchen worktop.
A London Fire Brigade spokesperson said: “Fires caused by refracted and reflected sunlight can happen all year round and are actually quite common.
“Our advice is to make sure that you keep mirrors, crystals, glass ornaments and other reflective items out of direct sunlight at all times.”
The Brigade was called at 4.10pm and the fire was under control by 5.13pm. Fire crews from Bethnal Green, Stratford, Whitechapel and Shoreditch fire stations attended the scene.