The arts venue said "all staff and public are safe" and that the building had been closed, following the fire on the Strand in central London on Saturday afternoon.
The cause of the fire, which was first reported just before midday, is not known.
London Ambulance Service urged people to avoid the area and told local businesses to keep their windows and doors closed.
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
A spokesman for London Fire Brigade said that crews are tackling flames located in part of the building's roof.
Two of the brigade's 32m ladders have been sent to the scene to support firefighting operations.
"The cause of the fire is not yet known," the spokesman said.
Fire wardens in hi-vis jackets escorted people away from the venue carrying signs that said "fire assembly point".
At least five London Fire Brigade vehicles were stationed outside the Somerset House arches on the Strand.
More fire engines could be seen inside the courtyard where thick smoke was visible.
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.
The building is currently used as an arts and events venue and was due to be hosting a day of breakdancing on Saturday.
The Courtauld Gallery, located in the North Wing of Somerset House, is home to a collection of famous paintings including Vincent van Gogh's 1889 self-portrait of himself with a bandaged ear.
Alan Robinson, 71, a Catholic priest who works nearby and lives in Covent Garden, said he was worried about the "irreplaceable" art collection in the gallery.
"The Courtauld Gallery is in there, I have no idea what the value of the collection is, but it's millions (of pounds) - irreplaceable stuff," he told the PA news agency.
The gallery also houses works by Edouard Manet, Claude Monet and Paul Cezanne.
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