and the same William in the 1911
but even further away from Arthur  
 
William Isaac Bradford
Age:   31
Estimated dob:   abt 1880
Boarder
Male
PoB LEWISHAM, Middlesex, England
Parish:   Islington
London
England
1 Colebrooke Row, Islington N
Married
Actor Drama
Reg dist:   Islington
Reg District No:   10
Sub-reg district:   Islington South East
ED:   61
Piece:   963
William Henry Bidwell   34
Bertha Bidwell   29
Thomas Bidwell   2
John Bidwell   0
Thomas Patton   48
William Isaac Bradford   31
I'm sure this is the William Bradford married to the Ethel Moir Crawford as the marriage parts of both of the 1911 censuses say the same - married 8 years,2 children 1 died.
This is him:
BRADFORD, WILLIAM  ISAAC     LAMBERT  
GRO Reference: 1879  S Quarter in GREENWICH  Volume 01D  Page 974