From her birth certificvate Ivy was actually born in Hampstead, not in Clapham which was her father's residence when registering the birth in September. That does make a difference in searching for her on the 1901 census. I'm fairly sure this is her with her parents in the 1901 census. Same number of children as in the photograph who look to be the right ages and with a potential difference in ages between the parents, which also looks right from the evidence of the photograph.
1901 census RG13 714 folio 132
Gravesend and Milton Union Workhouse
Grace Johnson Inmate married 29 wife of Joseph (crossed through) born Farnham Surrey
Then another inmate and the rest of the family
Joseph Charles Johnson inmate married 43 clerk in shipping house born Hackney London
Joseph Herbert Johnson inmate 7 Born Islington London
Edith Mary Johnson inmate 5 born Islington London
Ivy Johnson inmate 3 born South Hampstead
Gladys Johnson inmate 1 born Lewisham Kent
Elsie Mary Johnson inmate 1 month born Gravesend Kent
Workhouse information can be a bit out particularly with ages.
From FreeBMD
Births
possibly
Johnson, Gladys Caroline F 1900 March Births Lewisham
Volume 1d page 1267
pretty certain
Johnson, Elsie Mary 1901 March Births Gravesend
volume 2a page 604
The only possibility for a Joseph, on earlier censuses, who fits for age (within two years) and place of birth is
1891 census
RG12 219 folio 104
11 Fearhamtone? Buildings St Andrew and St George London
Johnson, Joseph C 35 Hackney, London, Head Married Lawyer's clerk
Johnson, Amy S 31St Giles, London, Wife Married
Johnson, Charles J 10 St Giles, London, Son
Given the difference in ages it would not be surprising if Joseph had married before, but without comparing a marriage certificate of your known Joseph to this Joseph to see if the father's name and occupation compare you couldn't be sure it is the same man.
1881 census
RG11 686 folio 118
2 Surrey Rd, Camberwell, London
Jos. C. Johnson abt 1856 Hackney Head Married Confectioner
Amy S. Johnson abt 1861 Bloomsbury Wife Married
Chas. J. Johnson abt 1880 Bloomsbury Son
FreeBMD
Marriages Sep 1879
Baker Amy Stocks Westminster 1a 861
Johnson Joseph Charles Westminster 1a 861
I can't find Amy or her son on the 1901 census or another Joseph born Hackney circa 1858/6. Pre the 1881 census I can't find a Joseph born Hackney, though there are other candidates born in the Hackney vicinity. You would need the information from the marriage certificates to search for Joseph and his father on earlier censuses.
Ruth Grace Fisher or Grace Ruth Fisher is still somewhat of a mystery as there is nobody showing of that age and place of birth on the 1891 or 1881 censuses. Perhaps ordering Elsie Mary's birth certificate may be useful to compare that given to the information on Ivy Adelaide's about her mother.
Regards
Valda