Fanny is on all the censuses as Fanny DIX (unmarried), born Salford/Chipping Norton, and there is a corresponding birth registration:
Births Dec 1866 DIX Fanny
Chipping N. 3a 660In addition, her son is registered as DIX, so I think you're safe in assuming that GLOVERESS is a red herring...

I remember this family from a previous search now - there's a whole tribe of them living together, and Fanny seems to be the illegitimate daughter of Hannah DIX. (But the birth cert should confirm that.)
Rambler