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%)
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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.