According to the charity, the blaze began in a building adjoining its headquarters in the early hours of the morning.
While the building was unoccupied and no casualties were reported, it said that both properties “suffered considerable damage”, the full extent of which is “still unknown”.
The cause of the fire is now under investigation, with the group working “closely” with the local fire service and agencies.
In a statement, the charity said: “While this is a major disruption, we’re fortunate that through our Covid-19 contingency planning we’re able to continue operations remotely and deliver online resources to provide as normal a service as possible.
“We’d like to extend our heartfelt thanks to Dorset and Wiltshire Fire and Rescue Service for their swift action in tackling the fire, and to our landlords Fonthill Estate, as well as our neighbours Messums and The National Trust for their support. We look forward to sharing further news when we know more.”