Four fire engines and 20 firefighters were called to Clink Street on Sunday morning to tackle a small electrical fire at the Clink Prison Museum.
The museum was evacuated but no injuries were reported. Part of the basement of the building was damaged by fire. The London Fire Brigade's investigators believe it was an accidental electrical fire.
The brigade was called at 10.32am and the fire was under control by 11.34am.
Fire engines from Southwark, Dowgate, Whitechapel and Old Kent Road fire stations were dispatched to the scene.
The fire brigade said on Monday morning that investigations are ongoing. The Clink Prison Museum is open to visitors as usual.