1881
Edward Goatley unmar 26 Tailor b Worcestershire (no relationship to head of family given)
living Lambeth with Barker family
RG11/622/85/45
1871
Edward Goatley umnar 16 apprentice Tailor b Worcester
living 12 Arthur's Tce - head is Samule Ponsford, Tailor
RG10/266/56/6
1861
And the most important one where I may find him with parents and siblings, I cannot locate him! But will keep looking.
This is the closest I could find on Freebmd:
births Mar 1852
Goatley Edward Worcester 6c 281
Of course if Edward is NOT Florence's father you may not wish to include Edward on your tree.

Her birth certificate may be worth purchasing as on her marriage certificate she may name Edward as he was her mother's husband, even if he was not her biological father.
I will leave the search there until you receive some more concrete evidence via certificates.