Hello Ian,
This looks like your family in the 1881 census:-
Dwelling: Private House
Census Place: West Newton, Northumberland, England
Source: FHL Film 1342239 PRO Ref RG11 Piece 5134 Folio 98 Page 9
Marr Age Sex Birthplace
Matthew SPENCE M 57 M Cornhill, Northumberland, England
Rel: Head
Occ: Agr Labourer
Margaret SPENCE M 57 F Cornhill, Northumberland, England
Rel: Wife
Robert SPENCE 14 M Chesterhill, Northumberland, England
Rel: Son
Occ: Scholar
They seem to have had another later son, Robert.
Here is another SPENCE family with the Head of the Household born in Wark and with the name Matthew in the family:-
Dwelling: No 2 Rows Cott
Census Place: North & South Gosforth, Northumberland, England
Source: FHL Film 1342231 PRO Ref RG11 Piece 5096 Folio 16 Page 23
Marr Age Sex Birthplace
Robert SPENCE M 37 M Wark, Northumberland, England
Rel: Head
Occ: Commercial Clerk
Hannah SPENCE M 30 F London, Middlesex, England
Rel: Wife
Charles P. EMERSON U 13 M Beringham, Warwick, England
Rel: S Son
Occ: Scholar
Edith EMERSON U 11 F North Shields, Northumberland, England
Rel: S Daur
Occ: Scholar
Matthew R. SPENCE U 5 M North Shields, Northumberland, England
Rel: Son
Occ: Scholar
Mary M. SPENCE U 3 F Walker, Northumberland, England
Rel: Daur
Occ: Child
Frances A. SPENCE U 2 F Kenton, Northumberland, England
Rel: Daur
Occ: Child
Mary STOBS W 79 F London, Middlesex, England
Rel: Mo In Law
Harry