About 125 firefighters and 20 fire engines tackled the inferno on Saturday and at 6pm crews were still "working to extinguish the final pockets of fire" at the iconic venue.
The Courtauld Gallery, home to priceless artwork, including Vincent Van Gogh's 1889 self-portrait showing him with a bandaged ear and paintings by Claude Monet and Paul Cezanne, was "unaffected" by the blaze and will reopen to the public on Sunday.
The cause of the fire, which was first reported just before midday, is not known.
There were no reported injuries.
Somerset House Trust director Jonathan Reekie said the fire broke out in the west wing of the building, which is mainly comprised of offices and "back-of-house" facilities, and there are "no artworks in that area".
The building is used as an arts and events venue and was due to be hosting a day of breakdancing on Saturday.
Michelle Birkby, 50, who lives in London and is a writer, was walking along the South Bank and could smell smoke.
"At first I assumed it was a barbecue in the courtyard, or some sort of event, but then I heard the fire engines, realised the smoke was billowing out of control and that Somerset House was on fire," Birkby said.
"It's a place I visit quite often and I know it's beautiful and I really hope they can stop the fire before it does too much damage."
Somerset House said on social media that the venue is currently closed due to a fire which has broken out in one small part of the building.
"All staff and public are safe and the site is closed. The London Fire Brigade arrived swiftly and we're working very closely with them to control the spread of the fire."
Somerset House is currently closed due to a fire which has broken out in one small part of the building.— Somerset House (@SomersetHouse) All staff and public are safe and the site is closed. The London Fire Brigade arrived swiftly and we're working very closely with them to control the spread of the fire.August 17, 2024
Queen Elizabeth I is among the former-stately home's previous residents, having lived there from the age of 20 before she became queen in 1558, according to Somerset House's website.
