I assume from your reply to Louisa Maud I have the correct family for William Joseph.
Between 1946 and 1992 there were only 3 Frank Wadam and 2 Francis deaths.
Of those only 2 were younger than William Joseph.
Frank J died 1949 Isle of Wight age 85 (1864)
Frank 1959 Brighton age 81 (1878)
Frank C 1965 Uckfield age 70 (1895)
Plus
Francis C 1955 Croydon age 85 (1870)
Francis W 1959 Poole age 95 (1864)
1881 - 34, Pier Road, Littlehampton, East Preston, Sussex + 5 siblings
Frank Wadham Son 3 1878 Scholar Littlehampton, Sussex, England
Walter Wadham father 44 1837 General Laborer Amberley, Sussex
Emily Wadham mother 34 1847 Felpham, Sussex
Frank Cecil Waddam born 1894 Woodstock MMN Allam he is with the family in 1901.
1901 Steeple Aston, Oxfordshire
Parents Richard age 35 mother Patience 35 + 5 siblings.
I’m not sure if you can find the connection and there is the possibility that Frank died after 1992.
Colin