Firefighters were called to the blaze at Gauntlett Court, near to Sudbury & Harrow Road station, on February 16.
A small part of a flat on the second floor was damaged by fire.
Crews rescued a man at the time who was taken to hospital for treatment.
However in an update issued yesterday (March 31), the London Fire Brigade says that the man died.
The brigade was first called to the scene at 6.19pm and the incident was under control by 7.43pm.
Over a month later, the cause of fire is still under investigation.