Fire has broken out at two water towers in Kew.
Four fire engines and about 20 firefighters have attended the blaze at the National Archives in Bessant Drive, next to the Thames.
The main building is not on fire but has affected a smaller adjacent building.
Video by Tom Hewitson (YouTube)
A Metropolitan Police spokesman confirmed they were called at 12.37pm and no injuries were reported.
National Archives UK tweeted: " Thank you for all your concerned tweets. We will update as soon as we can."
The National Archives is the Government's official archive of original documents and records, dating back more than 1,000 years.
National Archives UK tweeted later: " We can confirm the fire has been put out, but we will stay closed to the public in order to recover the building."
Zac Goldsmith, MP for Richmond and North Kingston, tweeted: "Very worrying news of a fire at the National Archives in Kew.
"Here's hoping the firefighters and extraordinary historic records are safe."
The National Archives is the official public archive of the British Government and holds records covering more than 1,000 years of history which have been selected for permanent preservation.
Contact the newsdesk: 020 8722 6392 / firstname.lastname@example.org.
TODAY'S TOP STORIES