Not in Northumberland but may be worth seeing if this one is on 1841/1851 Census at all;
Benjamin WALKER Baptised 26 Nov 1806, Holy Trinity, Sunderland, Durham
Parents JOSEPH/HANNAH Walker
Mother nee HERNSHAN
Fathers Occp Potter
Notes;
Benj 2nd son of Jos Walker of Stoke Sts by Hannah Hernshan of Doncaster
FileNumber 18272
(Source FreeREG)
I cant find any other Children to this Couple in Durham or Northumberland.
Trish

EDIT;
1841 Census
Pontefract, Yorkshire
HO107/1310/10/Pontefract
Joseph WALKER, 60, Potter, not born in County
Hannah, 55
Hannah, 20
Charles, 15, Potter
1851 Census Joseph is a Pauper born c 1779 Stoke, Staffordshire
Wife Hannah c 1783 Doncaster
So works with 1806 Baptism details.
Although Baptism may have Hannahs surname wrong (may have been hard to read for Transcriber)
Marriage Familysearch.Org;
Joseph WALKER to Hannah ERENSHAW, 17 July 1803, York, England