The Catherine who married George Shimmin, and whom Brian located in the 1891 census, looks like the daughter of William Quilliam and Margaret Redpath.

At 2 Lyddon Terrace in Leeds: RG12/3703 folio 124 page 9:
Elizabeth Downs Head Unm 48 Let appartments b London
Harriet Powell Wid sister 53 b London
Thomas Powell nephew 20 Unm Draper's assistant b Yorkshire
Catherine Quilliam (transcribed as William) serv Unm 19 General Domestic Serv. b Douglas
William Y Potter Lodger Unm 50 Curate St Andrews Leeds.

In 1901 at 29 Darlington St Leeds RG 13/4236
Thomas Frederick Elwick head mar 31 Carpenter & joiner b Leeds
Catherine A wife 29 b IOM
Ethel dau 7 b Leeds
Annie E d 3 b Leeds