I checked the 1901 Census, and found Herbert & his Sister:
RG13-3912, ED 19, Folio 159, Page 10
73 Carlisle Street, Blackburn, Lanc's
William GOLDSMITH, Head, Mar, 44Yrs old, Brushmaker , Bn Birmingham, Norfolk
Mary A. GOLDSMITH, Wife , Mar, 40Yrs old, Cotton Weaver , Bn Blackburn, Lanc's
HERBERT COX, Son in Law, Single, 15Yrs old, Apprentice Templatemaker, Bn Blackburn, Lanc's
ANN J. COX, Daut in Law, Single, 12Yrs old, , Bn Blackburn, Lanc's
It looks like Their Mother married again after their Father Died?
Found on FreeBDM:
Deaths June Qtr 1893
COX, James, 32Yrs old, Blackburn 8e 290
& this Marriage:
Sept Qtr 1899
GOLDSMITH, William & Cox, Mary Ann, Blackburn, 8e 928