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