Hello Ewan,
I see your problem. There were a number of Thomas Cox entries in the Birmingham area - including a painter whose name is on the back of a miniature I have of an ancestor from that area, who strangely enough was a gilder, carver, and print seller (1770-1842).
You have probably considered the possibility that William Henry left the IOM and returned to his wife sometime between 1901 and 1911?
The 1911 census has this entry:
COX WILLIAM HENRY M 1840 71 Wandsworth London. A "Helen" is in the household.
There are several with "Fanny" in the household, including:
COX WILLIAM HENRY M 1838 73 Tavistock Devonshire.
There is a death: Sep 1932
Cox Helen 85 Kensington 1a 189
[Her birth March 1/4 1847.]
As they were living in Islington in 1901 I'd be curious to know who this was: Deaths Jun 1906: Cox Ellen Maud 1 Islington 1b 159
And just to throw it into the mix, there is a marriage for a Maud N Cox Sep 1915 to Henry H Robinson Islington 1b 501 (I was looking for Maude Nellie Cox).
Sue