The likeliest candidate I see in 1851:
HO107/2132 492 7
Nottingham St Mary
31 Brougham Street
Martha Smith, head, wid, 34 (or 36?), Tambour?
Joseph Smith, son, 9, Cotton Winder
Susanna, dau, 6, scholar
Christopher Clarke, lodger, 13, Silk Mill
All born Nottingham