Hi again
Assuming that George and Hannah (Beck) are the right couple, this appears to be them:
1841 Shotley, Northumberland
HO107/842/1 folio 8 page 10
"Blanchland"
George Beck, 50, lead smelter, Y
Hannah, 50, Y
John, 25, lead miner, N
Thomas, 20, do., N
Mary, 20, N
George, 18, do. [lead miner], N
William, 15, do., Y
Jane, 10, Y
Joseph, 5, Y
1851 Shotley High Quarter, Northumberland
HO107/2414 folio 171 page 12
"Blanchland"
George Beck, head, 62, retired lead ore smelter, Blanchland Northumb.
Hannah do., wife, 63, Blanchland Northumb.
George do., son, un, 29, lead ore miner, <Eas-something> Durham
William do., son, un, 26, do., Blanchland Northumb.
Joseph do., grandson, 14, lead ore worker, Blanchland Northumb.
Jane do., daur, 20, Blanchland Northumb.
This does suggest that Hannah was indeed born in Blanchland.
Can't see George or Hannah in 1861.
But I guess you are aware that there's an Ancestral File and Patron Submission for her on the IGI, and that this says she died in 1858.