London Fire Brigade was called at 8am on Saturday to Amesbury Avenue and rescued a woman via an internal staircase using a fire escape hood.
Two people left the building before fire crews arrived and the fire was under control by 9.20am.
The emergency service said the fire is believed to have been accidental and caused by the failure of an e-scooter battery.
Mayor of London Sadiq Khan issued a fire alert last year amid concerns about privately-owned e-scooters and online conversion kits for e-bikes.
A London Fire Brigade spokesperson said: “It’s incredibly concerning we are continuing to see a rise in incidents involving e-bikes and e-scooters.
“When these batteries and chargers fail, they do so with ferocity and because the fires develop so rapidly the situation can quickly become incredibly serious.
“Lithium-ion batteries are susceptible to failure if incorrect chargers are used and there is a significant risk posed by e-scooters which have been converted.”
The fire brigade spokesman added that these are commonly seen sold on online marketplaces.
“Our advice is to try and store and charge these items in a safe location if possible, such as in a shed or garage, and if they have to be stored inside, make sure there is smoke detection fitted and your means of escape is not obstructed,” the statement added.
“However we know this won’t be possible for everyone, so if you are charging them indoors, please follow our advice on safe charging and ensure everyone in your home knows what to do in the event of a fire.
“We would also suggest people try not to charge them when they are asleep, so that if there is an issue they can react quickly.”