Thanks all for this!
The Whites and Halls were at the same address in the 1911 Census, but were on separate census pages so unknown if they were just all living together or the parents were a couple. However, in the Scottish marriage entry, Arthur does state that Jessie White, maiden surname Hall, is his mother. This is how I found him in the England census amongst all the other Arthur Whites.
I know that he says that he's single for his second marriage. The first marriage was legal, but there's no record of divorce so I guess he must have been a naughty boy and not mentioned his first marriage. I have no knowledge of how they would check these things across the 2 countries in those days.
Chempat - many thanks for tracking down the 1901 census entry, it does seem to be the same family, if a bit mixed up, and gives me the mother. Hopefully this should give me a bit more to go on.
The family tree on Ancestry was the Bartlett family tree, so I've written to the person who created it to ask if there is any family gossip on Arthur. I didn't bring up his first wife!
