Thick grey smoke could be seen billowing into the air from the landmark building, over the River Thames and nearby Waterloo Bridge.
Speaking to reporters, the LFB’s assistant commissioner Keeley Foster said firefighters carried out a “complex and technical response”.
They will remain at the scene into tomorrow, she added.
She was joined by Somerset House’s director Jonathan Reekie, who said: “It’s too early to comment on the building’s condition.”
He added the venue will remain closed until further notice, but the Courtauld Gallery will reopen to the public tomorrow.
In an earlier social media post, Somerset House said the venue was closed due to the fire, and all events on Saturday would not take place.
Following evacuation from the venue, staff and visitors were seen standing outside.
“Everybody is safe, there are no valuable artefacts or artworks in that part of the building,” Mr Reekie told the BBC earlier.
“For now we just want to let the London Fire Brigade get on and do their brilliant work.”
Due to heavy smoke, the London Ambulance Service asked people to avoid the area and told local businesses to keep windows and doors shut.
