Firefighters were called to Cotmans Close in Hayes just after 8.30pm on Monday (October 21).
Four fire engines and around 25 firefighters from Hayes, Southall and Hillingdon fire stations tackled the fire, which was under control by 9.18pm.
Part of the ground floor was damaged, and a garden shed was completely destroyed.
No one was injured.
Deputy Assistant Commissioner Paul Askew said: “Following a busy week of fireworks-related calls and incidents, we’re urging Londoners to follow our advice by attending a safer, organised fireworks display this year.
“If you are going to host your own display, it’s important to ensure you are buying safe fireworks from a reputable, licensed seller with a CE safety mark.
“Secure them properly in the ground, and keep them far away from buildings, trees, animals and people.
“Always follow the Fireworks Code and remember there are strict laws around when you can purchase and use fireworks.
“Never set them off if you’ve been drinking alcohol and once a firework is lit, never go back to it.
“Disposing of fireworks safely is just as important as using them correctly.
“Allow fireworks to cool properly before throwing them away.”
The incident came as the Brigade reported more than 1,300 calls since the weekend, including several fireworks-related fires across London – from trees and bins set alight to fireworks going off inside buildings.