I'm assuming that you don't have copy of her marriage certificate which I think you need to establish name of father (or not).
Also, how can you know that your 'Elizabeth' is indeed the Mary Elizabeth birth reg'd Mar.qtr.1874 Spilsby? In 1901 her birthplace given as Midville (but as far as I can tell from previous census' there weren't any Goslings born/living in Midville so perhaps it was her husband who gave this information in error). In the next census she states she was born in Nottingham?? Plus, in 1901 census shows bc.1874, next one bc.1875, and death bc.1876 and always as plain Elizabeth.
Definitely think you need to start with the marriage certificate to see what information can be gleaned from that but certainly don't think you can assume that the Mary Elizabeth birth 1874 is your Elizabeth.
Annette