Part of a four-roomed flat on the first floor of the building was damaged by fire. There were no reports of any injuries.
The fire is believed to have involved an electric scooter.
A London Fire Brigade spokesperson said: “Lithium-ion batteries, which are often used for e-bikes and scooters can be susceptible to failure if incorrect chargers are used. Always use the correct charger for the product and buy an official one from a reputable seller.
“Batteries can get warm during their use, so make sure to allow them to cool down before attempting to re-charge as they could be more susceptible to failure. Batteries should always be charged on hard flat surfaces where heat can dissipate.
“It’s a good idea to also ensure you have smoke alarms fitted in areas where e-bikes or e-scooters are being charged and make sure they are tested regularly.”
The Brigade was called at 2,24am and the fire was under control by 4,13am. Two fire engines and around 10 firefighters from Wimbledon and Tooting fire stations attended the scene.