Tracking down the elusive William Henry Ball has frustrating, but I am beginning to see a bit of light at the end of the tunnel. I took a chance and ordered a marriage certificate for Matilda K. Ball that appeared in the 1947 England/Wales marriage index.
Much to my delight - the certificate arrived and confirmed my suspicion... that Matilda had remarried in 1947. On 30 July 1947, Matilda Kate Ball married Bertram Cox in the Church of St. Mary in the parish of Cadoxton Juxta Barry, Glamorgan, Wales. Bertram was 54 years old, a widower, whose occupation was given as "Engineer". His father, John Cox (deceased), was also listed as an engineer. Matilda is listed as a widower, with no occupation. Her father, Charles Thomas Bowcher (deceased) is noted as a tipper. Bertram and Matilda were married by banns. Their witnesses were Grace M. Houd and Arthur W. Bowcher. Arthur, Matilda's brother, had witnessed her 1921 wedding to William Henry Ball.
Matilda and Bertram were noted as living at 17 and 19 Guthrie Street, Barry Dock. This is a map of their neighbourhood:
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and a link to a street view of Guthrie Street.
With Matilda's marriage, it now means that William Henry likely died between 8 December 1931, when he appeared as the informant on his father's death certificate, and 30 July 1947, when Matilda remarries. At least, I now have only a 16 year window to search!