Fifteen fire engines and around 100 firefighters dealt with a flat fire on Leman Street in Aldgate.
Two flats on the sixth and seventh floors of the building were alight. Firefighters led 11 people to safety. There are currently no reports of any injuries.
Borough Commander Lucy Macleod, who was at the scene, said: "Crews acted swiftly to bring the fire under control, but will remain on site this evening to damp down remaining hotspots.
“Road closures are currently in place, and there is significant congestion in the surrounding area. We urge the public to avoid the vicinity where possible while we continue to work to make the scene safe.
"One of the Brigade's 64-metre turntable ladders was used as an observation tower, providing a vantage point for incident commanders to assess the incident.
“We’re working closely with our partners to ensure support is available for residents affected by the incident.”
The Brigade's 999 Control Officers took the first of 15 calls to the fire at 1743 and mobilised crews from Whitechapel, Shadwell, Shoreditch, Dowgate, Bethnal Green and surrounding fire stations to the scene. The fire was under control by 1933.
The cause of the fire is under investigation.