Videos posted on social media show grey smoke billowing into the air from the landmark building, over the River Thames and nearby Waterloo Bridge.
The director of Somerset House Trust said the fire broke out in the west wing of the building and there are "no artworks in that area".
There are no reported injuries and the cause of the fire, which was first reported around midday, is not yet known.
London Fire Brigade (LFB) said the entire site at Somerset House has been closed to the public whilst the blaze is dealt with.
MNA
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