"Asbestos has not been confirmed at the site" said South Wales Fire & Rescue Service.
"However if asbestos is confirmed, this does not pose a safety risk to the public as heavy rainfall and water from firefighting will prevent the asbestos from spreading"
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Largely dry with clear spells overnight, but isolated wintry showers remain likely in the west.
A collection of thousands of Welsh newspapers have been moved to a new storage facility, along with millions of British editions.