Fire crew from four stations were called to the three-storey building in Leythe Road just before 1pm on Tuesday (October 31).
The man was rescued by firefighters from the first floor while six other people fled the building before the fire service arrived.
Four fire engines and 21 firefighters spent more 90 minutes battling the blaze which ripped through the block of flats.
A London Fire Brigade spokesman said: "Part of a flat on the first floor of the building and part of the communal hallway was damaged by fire.
"One man was rescued from the property by firefighters but he sadly died later in hospital A further six people left the building before the Brigade arrived.
"The fire was under control at 2.27pm.
The cause of the fire is under investigation.
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