So, to answer my own query:
John Joseph MARKHAM (1850 - ?) and Emma DAVIS (Abt 1853 - ?) married 24 Jan 1871 in Newington, Southwark, Greater London, England. They had seven children:
1. Elizabeth Marie MARKHAM (1870 - 1937) m. John TOMLIN (1870 - 1967)
2. John Joseph MARKHAM (1872 - 1930) m. Meriam JENKINS (1873 - 1954)
3. Mary Ann MARKHAM (1874 - 1949) m. William J. BUTLER (1869 - 1935)
4. Charles James MARKHAM (1876 - 1959) m. Dinah MESSEROLL (1875-1901); Elizabeth LUCAS (1875-1948)
5. Eliza Emma MARKHAM (1879 - 1958) m. William John COMBEN (1878-1924); William J. LEONARD (1872-1958)
6. Ada Emily MARKHAM (1881 - 1969) m. Robert DAVIS (1870 - 1938)
7. Marie Elizabeth MARKHAM (1884 - ?) m. William EVANS (1870 - ?)
From the obituaries of Elizabeth, Mary Ann and Eliza, all of the children were accounted for. Six of the seven were married in Hamilton, and many were witnesses for each other. Some named their children after their siblings. These facts are in stark contrast to reports of British Home Children being separated from family, never to be reunited. In many ways this is a good news story worth telling.
I am still curious to find more detail about Eliza, simply because of her connection to my family. Ultimately she left no descendants: she was first married at the age of 40 and remarried in her 50's. She never had children of her own. Once I have gathered all my data together and published a report I will contact Barnardo's Aftercare and ask if they will provide information to me on compassionate grounds.
Thank you to a vibrant genealogy community for all the help on this journey.