Four fire engines and 21 firefighters and officers were called to a fire at Milford Towers, Thomas Lane in Catford.
One van, 15 motorcycles and part of the service deck on the second floor of the building was damaged by fire.
Approximately 100 people from flats above the car park left the building before the arrival of the Brigade.
The Brigade was called at 0411 and the fire was under control at 0618. Fire crews from Lewisham, Forest Hill, Greenwich and Lee Green fire stations attended the scene.
The cause of the fire is under investigation by the Brigade and Metropolitan Police Service.