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Croome Court is a great NT property some 8 miles away - interesting house and lovely walks.
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Hope this helps, and enjoy your stay!
Speaking of National Trust; on our last trip to the UK we had great value from our membership of the Italian equivalent,
FAI - Fondo per l'Ambiente Italiano (the National Trust for Italy).
If you are a National Trust member you have exchange rights to use your membership in Italy.