I may have gone down a rabbit hole and not for the first time, but I have come to the conclusion that Elizabeth Kershaw Musk gave a false name when registering Alice so that she had her father's surname, Musk.
There are a number of Elizabeth Musk’s in the area at that time but I have been unable to find any tangible link to Alice.
Alice's BC says mother Elizabeth Kershaw Musk naming her as Alice Kershaw Musk, father's name omitted.
As I said earlier, I cannot find Alice Kershaw Musk in the census and she only appears with that name on her BC and MC.
(Alice's BC says mother Elizabeth Musk, no middle name Jane.)
In the 1881 census it shows an Elizabeth J Kershaw
Looking at the Lancashire BMD indexes for the year: 1861
Name: KERSHAW Elizabeth Jane
Mother: MARSDEN
Year: 1861
District: Darwen Blackburn
Elizabeth’s parents were Ann Marsden and Thomas Kershaw.
Elizabeth Jane Kershaw married a George Barnes in 1887 but died a couple of years later in 1889.
That is all the information I have in trying to discover who her mother was. Was she a Kershaw or a Musk?
Regards