Five fire engines and around 30 firefighters tackled a fire on Orchard Place in Leamouth.
Part of a flat on the first and second floors of an eight-storey block of flats was damaged by fire. Five people left the flat before firefighters arrived. They were assessed at the scene by London Ambulance Service crews for smoke inhalation. Four people left a neighbouring flat before firefighters arrived.
A 25-metre cordon was put in place to allow crews to deal with the incident safely.
The Brigade's 999 Control Officers received five calls about the fire.
The Brigade was called at 2048 and the fire was brought under control by 2247. Crews from Poplar, Plaistow, Millwall, Stratford and Shadwell fire stations attended the scene.
The fire is believed to have been caused by a lighter coming into contact with a combustible material.
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.”