Hi
I think I messed up with Edith's discharge in 1880 - it was from a Southwark workhouse - it probably says "To Aunt"
If so, possibly a maternal aunt, although Eugenia mentioned three sisters of Mr. Soffe I rather doubt whether she would have gone to one of them. Have you been able to find out anything about the Whitehorn family?
Eugenia seems to have been baptized at St Mary Lambeth, 15 April 1852. The name Dyer has come up in connection with the Whitehorns.
I would have thought Eugenia would most likely be somewhere in south London in 1881, but I haven't found her or her children anywhere. It's odd that Edith is still elusive (to me anyway!) in 1891.
If you are able to, I would think the best thing to do would be to try and get Edith's birth certificate.
JOHNSON, EDITH mmn WHITEHORN
1877 Sept Quarter in POPLAR Volume 01C Page 591
The children that Eugenia had after the split with William Soffe appear to have been registered as though the parents were married. Of course you never know for sure what it will say before you see it, but hopefully the certificate will name Mr. Johnson. It looks like that will be the only way you might get a line on Edith's father.
You'll also have her date of birth. Hoping she might still alive somewhere, you could try a search of the 1939 Register, looking for Edith's with that birth date. She probably wouldn't be Brown though.
It looks possible that history might have repeated itself, and that Edith split up from Herbert Brown sometime after 1901. If she then lived with someone else it would be very difficult to find her.
John