It is certain that the mother of Dorothy Cox was Una Ann Cadby. From her marriage certificate her father was Joseph Cadby, a Tool Maker of Bordesley. She was with her parents in the 1871 Census and the 1851 Census.
This establishes here parents as Joseph and Mary Cadby and her birth certificate confirms this.
  

        A search of the Death Index revealed only one possible death:
        1929-Q1 Cox, Una A age 78, Birmingham v6d p284
    

Known as Grandma
  

1890	40 Carpenter Road (Dorothy’s Birth certificate)
	    Alfred a ‘Merchant’s Clerk’ 

When she was married Dorothy's address was  Sherlock Street.

Family source : They kept a newsagents in Sherlock Street then moved to another shop near Hurst St.
When Fred died Una sold the shop to her cousin Alice Bannister and moved with her family to 15 Eldon Road.
By 1923 Mary, the daughter, had married.  Daisy was still at home adn when Dorothy married Ernest Phillips took over tenancy of the house.
  

In the 1911 Census Una Ann is described as a widow and was living with Dorothy and Daisy.
There appears to be only one death for Alfred Cox in the death index between 1901 and 1911.

It appears therefore that Alfred's death was registered in July-Sep 1909, in Birmingham.

However, the register entry for the marriage of Dorthy and Ernest does not appear to say that her father was deceased.

Searched on Ancestry for any details of burials but nothing found.
  

1901 164 Sherlock Street - Retail shop and house owned by George Goodman.
1906 164 Sherlock Street - Retail shop and house owned by George Goodman.
Mrs Una Ann Cox:
1911 6 Daisy Road - House and premises owned by Wm Sharp.