If this is your man in 1871
Piece 5155/ folio 18 /page 10
then by the 1881 census his wife (still living in the same place) is listed as a widow.
So he died between 1871 and 1881, Hartleyburn came within Haltwhistle civil registration district
Search Free BMD deaths, John Armstrong, Death age/DOB @1809-1813, died 1871 - 1881 Haltwhistle District
Brings up just 2 results
1 in 1873 age 64 and 1 in 1877 age 65
I'd guess that one of them is your man, but without the death cert I wouldn't like to choose which one
Boo