The blaze broke out in a stairwell yesterday afternoon.
The upper floors of the 22 storey building are empty, but around 20 people had to evacuate offices on the ground floor.
Firefighters say a discarded mattress caught fire after a cigarette or such like was not completely extinguished.
There were no reports of any injuries.
LFB says “if you’re a smoker, it’s absolutely vital you ensure your cigarette is completely out when you’ve finished smoking it.
If you don’t, you risk causing a fire which could not only destroy your home, but also cost you your life.”