i am not too certain about this bit 
in 1881 we have at Foundry Lane Hexham 
Thomas b. 1853 & his family
Francis b. 1848 & his family
and then your William b. 1833& Catherine and their children
now i have found Thomas & Francis in 1871 they are brothers.
Giles Gate 
George Young (he has been crossed out)
Thomas  22
Francis 18
Peter  16
: RG10;  5146;  12;  17;
i was hoping in 1861 they had a brother William and yes they do but i don't know if it is 'your' William his age is out somewhat and his occupation doesnt match  

Mickley Durham 
George Young   48 head widower hawker b. gateshead
William    20 coal miner b. Hexham 
George    18 do.
Ann    16
Thomas   12 scholar
Mary Jane 10 do.
Frances    8 do.
Peter    6
: RG9;  3857;  102;  8;
and in 1851 
George Young   40 head mar broomaker b. gateshead 
Jane Young   37 wife b. )do.
Isabella Obyusley   17 dau. married b. hexham
Margaret Young   15 b. New York 

 North. (short for Northumberland
John Young   12 tanner b. Durham Blue Quarries 
all other children b, Hexham 
William Young   10
George Young   8
Ann Young   5
Thomas Young   2
May J Young   4 months daughter 
Mary J Amsley    under 1 MOnth granddaughter 
 HO107;  2414;: 531;: 27
you really need to view the image it has something written on the address section i cant make it out