Ancestry's suggestion for Elizabeth born 1831 is a marriage to James Southworth. Lancs BMD has this as James Southworth / Elizabeth Porrit in 1850, Preston Register Office or Registrar Attended. This looks like the couple in 1851 and Elizabeth is the right age (19) but her birthplace is given as Walton le Dale:
1851 census on ancestry
The birthplace on that census was dittoed and she is listed in amongst James' family so the birthplace on the 1861 census is more likely to be right and it is Manchester:
1861 census on ancestry
274 North Rd, Preston, Lancashire (Three Tuns)
James Southworth Head Mar 31 Inn Keeper Lancashire Walton le Dale
Elizabeth Do Wife Mar 30 House Keeper Do Manchester
Ralph Do Son 8 Scholar Do Preston
John Do Son 6 Do Do Do
Ralph's birth on Lancs BMD shows MMN as Porritt to confirm this is the right couple.
In 1871 James and Elizabeth also have a daughter Margaret, 9, and sons Samuel, 7, and Peter, 4.
1871 census
Lancs BMD has an Alice Southworth, MMN Porritt, born 1856 Preston, and an Alice Southworth death in 1858 in Preston, age 2. So I would reckon this is the right Elizabeth as it means she named a daughter after her mother.