Five fire engines were called to Southwark Bridge Road on Sunday night when a fire broke out in a flat in the MyBaSE1 building.
Crews from Southwark, Dowgate, Whitechapel and Lambeth fire stations were called to the scene.
Southwark Bridge Road was closed to traffic and the 344 bus route diverted.
The London Ambulance Service also sent a crew to the incident.
Businesses in the building, including The Co-operative Food, were unaffected by the fire.
The cause of the fire is under investigation.
Firefighters will hold a protest march from the Monument to LFB headquarters in Union Street on Thursday lunchtime.