Good day! I have just received additional information from Nottingham Uni !!
"I have located Alice in two registers, as follows:
Register of Births (ref: Uhh P 7/1)
Date 6 Feb 1899
Name of parents, or mother: Hall, Harriett
Parish from which admitted: Ilkeston
In what name baptized: Alice
Admission and Discharge Register (ref: Uhh P 1/1)
Date 6 Feb 1899
Name: Hall, Alice
Calling, if any: None
Religious persuasion: Methodist
When born: 5.50am
Parish from which admitted: Ilkeston
By whose order: Born
If born in House, name of mother or parents: Harriett
I am afraid that the name of the father is not recorded."
In addition, I received an email this morning from GRO refunding the fee for Alice's birth certificate, as they say there is no record of her. I'll try again as I had indicated that her name was "Fisher or Hall" and I'm not convinced that they would have searched for "Hall".
Digging continues ...