Have just found florence on census for 1891 known as Annie, described as wifes daughter by John Balkwell.
1901 she is living with her grandmother Harriett and uncle John, census transcription shows her as granddaughter, and Beatrice is Beatty granddaughter.
So looks as if John B might not be the father. Marriage cert might give a clue especially if it says deceased. Sorry cant get any nearer.