Hi lazylane,
Welcome to Rootschat

FreeBMD has 2 possible birth registrations:
Isabella Matilda Miller DecQ 1856 Lambeth 1d 252
Isabella Miller SepQ 1858 Lambeth 1d 270
The one registered in SepQ 1858 is possibly your lady; copy of the birth certificate should show her parents.
1881 census has an Isabella Miller b1857 Lambeth living at home with parents and siblings in Lambeth.
William Miller Head 58 Perthshire, Scotland Stone Mason
Isabella Miller Wife 56 " "
Grace " da 25 Lambeth Domestic at home
Isabella " " 22 " Artist Potters
William " s 20 " Clerk to Iron Merchant
John " s 18 " Clerk to Tanners
and a lodger
Arthur S Brown 25 Off Cape of Good Hope Clerk Civil Engineer
All at 136 Kennington Rd, Lambeth Surrey
RG11 0594/112 22
Nanny Jan