Hi Jeff; welcome to Rootschat!

At the start of each census is the route the enumator took. You might be able to zone in on it from it's surrounding streets.
Using a random address on Hamilton St., the 1881 enumerator for at least part of Hamilton, used this route:
Left hand side of Collyhurst Street from Hamilton Street to a point of the boundary line near the "White Hart Inn" along the boundary line to near the top of Percival Street.
Continue along the boundary to a point in a line with Churnet Street. Left hand side of Churnet St. to Hamilton St.
Left hand side of Hamilton St from Churnet St. to Collyhurst St. including all the Houses, Courts, etc within the aforesaid boundary.I get lost on maps, so I have not compared it the map Ray T provided.