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.
More top news
With just three days to go until polling stations open, representatives from all parties were out in force across the capital today.
The garden above the Canary Wharf Crossrail station is now open to the public.
First time buyers in London now need an average annual income of £77,000 - nearly double the amount required in the rest of the country.