Sorry, I got my generations a bit mixed when visualizing the strict grandmother.
The only other idea I have had in the meantime is electoral rolls.
There are often some avialble at local record offices, and they can be a boon to tracing peoples movements in latter years.
Bearing in mind there are probably several Arthur Brain's around (There seemed to be loads when I tried to look for his second marriage) it might be best to first try and find the family pre Gwennie's marriage - but after she is 21 - thus finding Gwennie, and therefore the correct family. A bonus may be to find stepmum's Christain name, and if step siblings are over 21 then them aswell.
But really I was thinking this would give you the address of the famliy. Youcould then trace this address through whatever years they have electoral rolls available.
if the whole family moves, it wont help, but if they continue to be registered there after Gwennie leaves, and then at some point Mrs Brain continues to be registered there but no Arthur, then it might just indicate that he had died (he could of course have left her). Thus narowing down possible years.
bu tI dont know where you are, and whether a trip to the Local Record office is feasible. Yoy might like to email them first to see what info they have and how much in the way of look ups they will do for you. Or even before that, you may find out a bit more from local Rottschatters on the board which covers Ferry Hil, Co Durham. Sorry - not my part of the world at all!
Hope you eventually, by some means or other, find his death! It is a trivky one, cos even if you send for a death cert (e.g the one you found in the indexes at beginnig of theis thread!) you will have no way of knowing if it is him or not - it will probably be registered by his wife or child - neither of which you know the names of. so without 'filling out' more info about his life I dont think you can meaningfully find his death.