I have just seen your message and I don't know if you have progressed since!
My ancestor is John Dixon Stimson, born in 1848 in Brighton and he is Jane Harriet's brother. I only know their parents are Edward Stimson (b.1819-1895?) and Matilda Barrett (1818-1897?), they married on December 13th 1840 at St Nicholas (Brighton) and that their respective parents are John Dixon (another one) & Harriet Stimson and James & Jane Barrett. I would appreciate any other information!
As for the Igglesdens, I have found that James and Ann Simpson married on August 7th 1836 at St Nicholas. I have also another child of Henry and Jane Harriet : Flora, b. 28.08.1874 and baptized 06.12.1874 at St Leonards in Shoreditch. But I have not really looked for that part of the family because I am not related to them directly. Sorry I can't help more.