On the 1891 and 1901 census Kate Embury is listed as being born in London. 
 
The only Kate Miller I can find born in London on freebmd is in Sept qtr 1850 - may be too early.
 
Here is the freebmd link in case you don't have it.
 
https://freebmd.rootsweb.com/
 
Here is the London birth and Kate's marriage to George
 
Births Sep 1850   (>99%)
--------------------------------------------------------------------------------
 
Miller  Kate    Petworth  7 483    
Miller  Kate     W Ham  12 313    
Marriages Mar 1880   (>99%)
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Ellis  John    Birmingham  6d 73    
Embury  George     Birmingham  6d 73    
Miller  Kate     Birmingham  6d 73    
SMITH  Annie     Birmingham  6d 73    
You can use these details to order certificates to help your search.