Twelve fire engines and around 80 firefighters tackled a fire on Hindmarsh Close in Shadwell.
Most of a 15th floor flat in a 24-storey block of flats was damaged by fire. Half of a neighbouring flat was also damaged by fire. Around 40 people left the building before firefighters arrived. Around 20 people were led to safety by firefighters. There have been no reports of any injuries.
People in the area were advised to keep windows and doors closed whilst firefighters worked to extinguish the fire.
Station Commander Steve Irvine, who was at the scene, said: "A respite centre was set up locally for those who have been affected by the fire.
"Road closures were in place in the area and we asked people to avoid the area whilst the incident was ongoing."
The fire is being treated as accidental. The most likely cause is a discarded cigarette that blew onto a balcony and ignited material stored on it.
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 properties but also cost you your life."
The Brigade's 999 Control Officers received 71 calls about the fire and the gave vital fire survival guidance to a number of residents before firefighters arrived.
The Brigade was called at 1216 and the fire was brought under control by 1326. Crews from Shadwell, Whitechapel, Shoreditch, Dockhead, Millwall and surrounding fire stations attended the scene.
Firefighters' smoking safety tips
· Use proper ashtrays, which can’t tip over and stub cigarettes out properly.
· Don’t leave lit pipes or cigarettes unattended.
· It's safer to smoke outside, but make sure cigarettes are put right out and disposed of properly.
· Don't balance cigars or cigarettes on the edge of an ashtray, or anything else – they can tip and fall as they burn away and cause a fire.
· Take extra care when you’re tired, taking prescription drugs or if you’ve been drinking alcohol.
· Always empty ashtrays carefully. Make sure smoking materials are out, cold and preferably wet them before throwing into a bin – never use a wastepaper basket.