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