I wonder if this maybe a possibility for your Edward born c1863 on 1871 census
named as Edwin his father's name is William and his occupation is General Labourer
1871 census Piece:1623 folio:84 page 5
Living 27 New Street Stratford West Ham
William Walker (1821) Dagenham Essex
occ General LabourerMary (1822) Navestock Essex
Alfred (1856) Stratford Essex occ Factory Boy
John (1861) pob dittoed
EDWIN (1864) pob dittoed1861 census Piece:1059 Folio:13 Page 40
Living 5 Duckham Cottages
Wm Walker (1824) Dagenham Essex
occ Dock LabourerMary Ann (1825) Navestock Essex
Willm (1854) West Ham Plaistow Essex
Alfred (1856) pob dittoed
John (1861) pob dittoed
will see if I can follow William
Mmm... had no luck finding William pob Dagenham on 1851 census

I've been searching for them in 1891 for ages today,but had no luck.
I can't find Edward, Fanny, Alfred & Edward Walker either on 1891 census

Father Edward's pob Canning Town Essex & Bow London - not making it easy

I'm wondering if this his him on 1881 census
Edward Walker Lodger b1863 London Middx
occ Labourer1881 census
https://familysearch.org/pal:/MM9.1.1/X3LT-PN7I see what you mean pob