On Thursday night, almost 70 firefighters and ten fire engines responded to the fire on Rymill Street in North Woolwich.
According to London Fire Brigade, the majority of a three-room apartment on the tenth story was damaged.
It further stated that 100 inhabitants were transferred to a nearby rest center, and four individuals were guided to safety by fire crews.
Its control center received about thirty calls regarding the fire.
About 10.30 p.m., the brigade received word of the incident, and shortly before midnight, the fire was brought under control.
Investigating the cause of the fire is underway.