Alice wa illegitimate. However, she appears to have had family: John Mather; Elizabeth Mather (X) were her marriage witnesses.
The 1855 birth record suggests Alice is a bastard child.
In 1871, Alice and Thomas (16 and 8) were with their grandmother Hannah (66). Jane (30) and John (21) were also present and Jane is the likely mother (John is too young).
Alice may be another illegitimate daughter of Alice Mather.
Alice and James were married in a religious ceremony on May 29th, 1874 at Christ Church, Walmsley by R C W Croft and witnessed by John Mather & Elizabeth Mather.2
Marriage/Union Notes
Marriage: 29 May 1874 Christ Church, Walmsley, Lancashire, England James Naylor - Full, Spinner, Bachelor, Walmsley Alice Mather - (X), Minor, Spinster, Walmsley Groom's Father: John Naylor, Spinner Witness: John Mather; Elizabeth Mather, (X) Married by Banns by: R. C. W. Croft Incumbent Notes: ['Illegitimate' noted where the bride's father's name would be recorded] Register: Marriages 1854 - 1887, Page 144, Entry 287 Source: Microfilm of register at Manchester Library