Smoke was seen rising over central London from the building's roof as firefighters worked from a crane to douse the flames.
The building was once home to the Royal Navy but is now used as a cultural center. A gallery inside the complex houses Vincent Van Gogh's self-portrait of himself with a bandaged ear.
Somerset House Trust director Jonathan Reekie told Britain's PA Media that the fire broke out in the west wing of the building, where offices and back-of-house facilities are located. There are "no artworks in that area," PA Media reported Reekie as saying.
Around 125 firefighters and 20 fire engines were deployed to Somerset House, according to the London Fire Brigade.
The crews fought flames located in part of the building's roof, the fire brigade said in a statement, with two of the brigade's 32-meter (nearly 105 foot) ladders being used. It said the brigade had been called shortly before midday and had brought the fire under control by shortly before 7 p.m. local time.
The cause of the fire is not yet known, the statement said, and Somerset House has been closed to the public.
The complex was first built in the 1500s, though it was demolished and rebuilt in the 1700s.
The house gets its name from Edward Seymour, Duke of Somerset, who built it as a palace for himself in 1547. The Duke was executed at the Tower in London a few years later, and ownership of his palace passed to the Crown.
In 1604, the Treaty of London was signed within the building, ending the 19-year Anglo-Spanish War. It later served as the headquarters for the parliamentary army during the English Civil War, and narrowly escaped burning in the Great Fire of London in 1666.
Somerset House is now the host of creative events and exhibitions. It is home to the Cortauld Gallery, which counts works by Manet, Van Gogh, and Monet among those in its collection. Kings College London has its school of law in the complex's east wing.
It has served as a versatile filming location and can be spotted in the backdrops of films and TV shows like 'Downton Abbey,' 'Love Actually,' and 'X Men: First Class.'
On Saturday, it said a dance battle was supposed to be held in the building's open air courtyard, with "a day of dance and breaking showcases, workshops, live DJs and a big outdoor party, all culminating in a head-to-head dance battle between the four corners of London."
"All staff and public are safe and the site is closed," Somerset House said in a statement on its website.
The London Fire Brigade said its crews would remain on scene into Sunday.
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