Dear Peter,
I found the following family in the 1881 Census.
Robert BLACK Head M Male 45 Carlisle, Cumberland, England Carpenter Empl 3 Men & 4 Boys
Louisa E. BLACK Wife M Female 41 Carlisle, Cumberland, England
Robert H. BLACK Son Male 8 Carlisle, Cumberland, England Scholar
John H. BLACK Son Male 7 Carlisle, Cumberland, England Scholar
Address 7 Myddleton St
St Cuthbert W/O - Botchergate, Cumberland, England
Bothergate is part of Carlisle