I just realized I missed the part about your great-grandfather being "Arthur".I guess David's father is not your grandfather.
I show 3 different Arthur Dunford's:
Arthur Dunford, born 1899 in Peterborough
Arthur Dunford, born 1883...he married Elsie Butterworth
Arhtur Dunford, born 1874 in Ketton, Rutland
Do any of these match your great-grandfather?By the way, where are you located?We have Dunford relatives that are still in England, some that went to Australia, and some (my branch) that came to the US (Michigan).I'm currently in CA, but from Michigan orig.