Eight fire engines with around 60 firefighters responded to the incident on Windsor Road.
In a statement the London Ambulance Service said: “Firefighters tackled a fire at a two-storey mid terraced house, which was completely destroyed by the fire.
“Four people, two adults and two children, left the property before the Brigade arrived.
“Luckily the family were awoken by smoke alarms fitted in the property, which alerted them to the fire and they were able to get out.
“The family were treated for smoke inhalation at the scene by London Ambulance Service.
“The Brigade was called at 0104 and the fire was under control at 0241.
“Fire crews from Stratford, Leytonstone, Plaistow, East Ham, Ilford, Leyton and Poplar fire stations attended the scene.”
The cause of the fire is currently under investigation.
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A London Fire Brigade spokesman said: “The fire was discovered by an employee of an adjoining warehouse who smelt burning and saw smoke coming from the roof of the warehouse next door. They then made the first of 36 calls to the Brigade.
“The warehouse blaze produced a lot of thick black smoke and we asked anyone in the local area or driving past to keep their windows closed.
“Firefighters worked throughout the night to make the scene safe.”