Diane,
Re The Chestnuts. The photograph is of the original house, that was called The Chestnuts, and was on Garretts Green, where the Church now stands. The Chestnuts Public House was named after it, but the pub was not built on the site of the old house. And is, as you said, on the corner of Garretts Green and Sheldon Heath.
Hope your mom can shed some light on Annveitch's white house. It maybe the one Len mentioned.
Ann