Hello Pinetree
I have recently started building a family tree and I think you may have just given me another generation in my late father's family.
My paternal grandfather was Ernest Edward Mims, born 1866 in Berkhamsted. As far as I can make out from the Genes Reunited site, his father was James Hawley Mims, born 1829 in Fenny Stratford. It seems he married someone called Elizabeth Gee, born 1831 in Newport Pagnell. They may have married in 1851 in Shoreditch (not sure about this and why not marry more locally, although there does seem to be some family link to Shoreditch*).
Anyway, I wondered if James Hawley Mims (my great-grandfather) was another child of John Mims and Harriet Hawley, and so a younger brother of Martha.
As far as I can tell, one of James Hawley Mims' sons was James Henry Hawley Mims, and one of Ernest Edward's sons was Edwin Hawley Mims (i.e., my uncle, although he died before I was born). The last fact is certain because I remember that my father had a silver (christening?) cup engraved with his name.
Most of the above is from cross-checking easily available records, so not verified beyond my uncles, aunts and grandparents.
Does any of this fit with your research?
With best wishes
John Mims
*Somewhere I found that one of James Hawley Mims' sons, Frederick Bosworth, lived with his aunt Elizabeth in Islington. Elizabeth was given as being born in Fenny Stratford in 1815, so possibly another of Harriet and John's offspring. Elizabeth's children were shown as being born in Shoreditch.