Part of a first-floor flat in an 11-storey residential block in Wanborough Drive was damaged in the blaze.
Two adults and a child were rescued from the flat’s balcony by firefighters using a ladder.
The fire is being treated as accidental and is believed to have been caused by the failure of a lithium battery pack on an e-scooter.
The e-scooter was stored in the hallway and was not in use and not on charge at the time of the fire.
E-bikes and e-scooters have become London’s fastest-growing fire risk.
There was a fire in the capital involving these types of vehicles, on average, once every two days last year.