A fire service spokesman said the whole of the roof of the museum and library was on fire.
Station Manager Peter Critchell, at the scene, said:
"Flames are coming through the roof and there is thick grey smoke billowing up. Firefighters are still working hard at the scene to try and bring the blaze under control. We now have water jets attacking the fire from the four corners of the building. We evacuated 30 people from inside the museum and firefighters will be making efforts to salvage as many of the artefacts as possible."
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The plaque at number 16 Cowley Street in Westminster marks the brown brick Georgian townhouse where Sir John lived for 31 years.
A man reportedly armed with several knives has been arrested in Whitehall on suspicion of planning a terror attack, police have said.
Metropolitan Police officer, Tom Harrison, has been crawling the course since the race began on Sunday morning.