Many thanks to the diligent and resourceful Tim Wilkinson for pointing out that the Wiltshire Archives have posted some local burial records online.
Wonderful to see that William and Ann Budd’s burials, both in Bremhill Church nearby to Studley in Wiltshire are there.
Copies below.
This confirms the line of enquiry that placed William and Ann in Studley (living in Rumsey Cottage in the grounds of Rumsey House where their eldest daughter lived with her husband Benedict Angell) from 1810 until their respective deaths in 1821 and 1825.
Budd Family Tree 