More than 80 firefighters tackled the blaze at the leading venue; the grand hall has been destroyed
Everyone is believed to have evacuated the building safely, with a tweet from the BAC account reading: "There is a fire in our building. Everyone is out safe and the fire brigade are working hard to get the fire under control."
London Fire brigade tweeted: "12 fire engines and 80 firefighters now tackling the art centre fire in Battersea."
The fire began at approximately 4.15pm in the roof of the cultural hub in Battersea, a Victorian Grade II* listed building. Smoke could reportedly be seen from as far away as Millbank.
Battersea Arts Centre on fire. Fire service putting it out. pic.twitter.com/Gl7kjMPRfN
— Andrew Stanford (@ResiPropertyMan) March 13, 2015
More than 50 calls were taken from the fire brigade's call centre about the blaze. The building has been undergoing renovation works as part of a £13 million project to add an extra floor and remove partition walls.
A London Fire Brigade spokesman said: "The cause of the fire remains unknown and the situation is very much ongoing."
Two aerial appliances are fighting the fire, which is affecting the back of the building and its roof, from above.
There is an ambulance on standby at the scene, but no people have been reported injured. The roof of the Grand Hall, the venue's biggest performance space, is believed to have been destroyed.
A commuter posted the following video on YouTube, showing the extent of the blaze.
All performances at the venue on Friday evening – including Fiction and Missing – have been cancelled, and Saturday's performance of Missing will also not go ahead.
Battersea Arts Centre is a registered charity, raising 70% of its income through donations and sponsorship each year. The building originally opened in 1893 as Battersea Town Hall, and it was converted to an arts centre in 1974.
BAC recently announced plans to merge with the nearby Wandsworth Museum, and unveiled a new season featuring guest performances from over 30 companies from across the country.
Update: Artistic director David Jubb posted the following message on Saturday:
"Yesterday there was a fire at Battersea Arts Centre that destroyed the Grand Hall and Lower Hall.The organisation and the front half of the building live to fight another day. We start now.
"As I cycled towards the building last night I thought about the millions of people who have shared and enjoyed the Grand Hall and Lower Hall over the last 120 years – as a public space – for everyone. These public spaces are reducing in number – which makes it all the more heartbreaking.
"Huge thanks are owed to all the emergency services, who literally saved the front half of the building, to staff, artists and volunteers at Battersea Arts Centre, and to everyone who has shown their overwhelming support online over the last 24 hours. The passion for the building and the organisation is extraordinary. Thank you all for being part of this. We really need you at this time."
A fundraising page has been set up at nationalfundingscheme.org.