100 firefighters tackled the blaze in Blueberry Court on Broadis Way at 5.45am today (October 24).
A video taken by a bystander shows flames erupting out of the windows of the block of flats in the dark.
Firefighters can be seen running towards the burning building.
A later video shows water being sprayed on the smoking and smouldering remains of two flats that were burned in the incident.
Two balconies were destroyed in the blaze and parts of flats on the third and fourth floor were damaged.
There were no reports of any injuries.
A rest centre was set up at Mardyke Community Centre.
Firefighters from Dagenham, Tottenham, Wennington and other surrounding fire stations brought the fire under control by 7.28am.
The cause of the fire is under investigation.
