Thanks Raffaele and Coromandel for your input.
@Coromandel: the photo is a head and shoulders profile shot of Bill with a nondescript background. A young man in an Edwardian suit, no further hints, I'm afraid.
For me, one of the most frustrating things is that we lost contact with someone as recently as 1920 ... mind you, my grandfather lost contact with all his UK-based relatives after he left in 1920.