The fire damaged the majority of a four-room flat on the ground floor and a small portion of another flat on the first floor. Before the Brigade arrived, three men left the ground floor flat. London Ambulance Service crews transported one man to the hospital.
The Brigade's 999 Control Officers responded to 19 calls about the fire.
"On arrival, crews faced a fully developed and very visible fire," said Sub Officer Kim Jerray-Silver, who was on the scene. The flames were about a metre away from the window.
"Crews worked extremely hard to quickly put out the fire." They searched the building to ensure that everyone was safe and to reassure residents."
The Fire Department was called at 9.07am, and the fire was out by 10.34pm. Firefighters from Chiswick, Acton, North Kensington, and Richmond were dispatched to the scene.
The fire is thought to have been started by accident.