Ten fire engines and around 70 firefighters were called to a fire at a block of flats on Acorn Way in Farnborough.
Part of the roof of a three-storey block was damaged by the fire. Around 15 people left the building before the Brigade arrived. One woman was treated at the scene for smoke inhalation by London Ambulance Service crews.
Station Commander Jim Berry, who was at the scene, said: "The roof of the building was well alight when firefighters arrived.
"Crews used one of our 32m ladders to put water on the fire from above.
"Local road closures were in place so we advised motorists to avoid the area where possible."
The Brigade was called at 0636 and the fire was under control by 0828. Fire crews from Orpington, Bromley, Biggin Hill, Beckenham, Addington and surrounding fire stations were at the scene.
The cause of the fire is under investigation.