I had a look at the 1881 Census for 51 Willow Walk, Bermonsey and it appears that your COOPER's have been transcribed wrongly either by the enumerator or the person who transcribed the entry as HARBOUR for some reason or the other but I would say from the names and occupation of the father 'TANNER' and Alice aged 3 and another Rose aged 5 also wife Mr must be mary that they are your family I suggest you look at the original.
Dwelling: 51 Willow Walk
Census Place: Bermondsey, Surrey, England
Source: FHL Film 1341127 PRO Ref RG11 Piece 0561 Folio 24 Page 42
Marr Age Sex Birthplace
Wm. HARBOUR M 35 M Lewes, Sussex, England
Rel: Head
Occ: Tanner
Mr. HARBOUR M 40 F Lewes, Sussex, England
Rel: Wife
Annie HARBOUR U 9 F Bermy, Surrey, England
Rel: Dau
Occ: Scholar
Geo. HARBOUR U 7 M Bermy, Surrey, England
Rel: Son
Occ: Scholar
Rose HARBOUR U 5 F Bermy, Surrey, England
Rel: Dau
Occ: Scholar
Alice HARBOUR U 3 F Bermy, Surrey, England
Rel: Dau
Arthur HARBOUR U 2 M Bermy, Surrey, England
Rel: Son
Hy. HARBOUR U 19 M Whitechapel, Middlesex, England
Rel: Boarder
Occ: Smith
Hope this helps
Roma