Southwark Council leader Peter John says the the fate of items in two galleries at the Cuming museum is 'unknown at present'.
Firefighters tackling the fire at Walworth Town Hall are currently damping down.
On twitter, Councillor John paid tribute to the London Fire Brigade and to Southwark Council for their efforts in trying to save the museum's collections.
Amazing work by LFB and Southwark Council museum staff to remove Cuming Museum artefacts from Walworth fire today.
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The man is believed to have suffered a fractured cheekbone.
The man, who was in his 30s, has not been identified, while several other people are believed to have suffered serious injuries.
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