Four fire engines and around 25 firefighters tackled a fire on Denholme Road in West Kilburn.
A lean-to structure in a garden was destroyed by fire. Part of a ground floor flat in a two-storey house that has been converted into flats was also damaged. There have been no reports of any injuries.
The Brigade's 999 Control Officers have received 39 calls about the incident.
The Brigade was called at 1333 and the fire was under control by 1442. Crews from North Kensington, Paddington, Willesden and Acton fire stations attended the scene.
The cause of the fire is under investigation.