The marriage you found is correct Karenlee;
1851 Census
Mott St
Birmingham/Warwick
HO107/2058/411/15
Thomas GRIFFITHS, 23, Mar, Gun Finisher
EMMA, 23, Wife, Mar
Both born Birmingham and living a couple of doors down from Sam/Cath

1871 they are in St Mary Whitechaple, London, with Daug Hannah born c 1853, Birmingham. He is a Gun maker.
I havent found them in 1861
(just realised I'd posted 1851 instead of 1861!)