Four fire engines and around 25 firefighters were called to a fire at a flat on Hirst Crescent in Wembley.
Part of a flat on the first floor of a four-storey block was damaged by the fire. Two people left the building before the Brigade arrived. One woman suffering smoke inhalation went to hospital as a precaution.
The Brigade's fire investigators believe the fire was accidental and caused by items too close to a heater.
A London Fire Brigade spokesperson said: “Fires involving heaters like this are all too common. They usually start when items, like clothes or bedding, are placed too close to the heater and ignite.
“It’s absolutely vital that heaters are kept well away from curtains, bedding or furniture and are never used to dry clothes.
“It's also important to always sit at least a metre away from the heater, as it could set fire to your clothes or your chair, and position them where they won’t be knocked over."
The Brigade was called at 1145 and the fire was under control by 1238. Fire crews from Wembley, Park Royal, Southall and Northolt fire stations were at the scene.