I'm fast running out of ideas, Danuella There are three birth reg. on FreeBMD in Croydon in the name of Bishop with the mother's maiden name as Bishop;
Mary Bishop Q1 1912 Eileen V. Bishop Q3 1917 Winifred N. Bishop Q1 1923
If Minnie never married Frank Fairman but continued to live with him as his wife then all children born of that partnership would be registered in her name of Bishop. We don't know for sure if there was a birth reg. for Minnie Bishop in Croydon about 1881 as the FreeBMD is incomplete.
I discounted the other Minnie as she was with her mother in 1901 - yet daughter Rebecca was b 1900 but was not living with them and there was no other entry for a Rebecca Bishop that fitted the profile