Around 100 firefighters tackled the huge blaze at the business centre on Fairfield Road in Bow just after 6pm on Friday - the blaze was put out at around 8.48pm the LFB said.
Half of the flats on the fifth and sixth floors of the building were also damaged, the London Fire Brigade (LFB) said.
Fifteen people left the building before the LFB arrived but there are no reported injuries.
One of the Brigade’s 64m turntable ladders and a 32m turntable ladder were deployed as water towers to tackle the flames from height and road closures were put in place to allow crews to work safely.
Assistant Commissioner for Operational Control and Resilience, Pat Goulbourne, said: “This was a challenging and complex fire but our crews worked quickly and tirelessly to restrict damage to homes and ensure that no one was hurt.
“Our Control Officers took 123 calls about this incident and responded quickly, with a fire engine on scene three minutes after the first emergency call was received.
“At the same time, we were also dealing with another significant fire elsewhere in London. However, our Control Officers are trained to manage our resources as emergencies occur, and appliances were strategically moved across London to ensure the affected areas had appropriate fire cover to allow us to continue to respond to emergencies.”
Fire crews from Bethnal Green, Whitechapel, Homerton, Shadwell, Islington, Plaistow, Shoreditch, Lewisham and surrounding fire stations attended the scene.
The cause of the fire is under investigation.