As they have a Mary Holding, relative living with them in two of the census, I wonder if she was Ann's sister. If so this marriage is a possible especially as they had their first child in Leicester.
LIVERS, William
Registration district: Leicester
County: Leicestershire
Year of registration: 1838
Quarter of registration: Oct-Nov-Dec
Volume no: 15
Page no: 195
MarriageFinder William Livers married one of the following people Transcript
BIRCHALL, Jane VIEW
HOLDEN, Harriett Ann VIEW
ADAMS, John VIEW
Barbara