The fire damaged two unused water towers at the site in Kew. The BBC said an estimated 11 million documents -- some more than 1,000 years old -- are stored at the site.
A spokeswoman said everyone inside the archive was evacuated safely and no damage was done to the building's contents.
The National Archive was closed to the public after the fire. The cause of the fire was under investigation.
Notable deaths of 2014 [PHOTOS]