Freebmd has 2 Florence Gertrude McDonald births - Dec 1885 Lambeth & March 1892 West Ham
This looks like the Lambeth family, which would tally with the Who's Who entry.
GRO BMD references:
1874 Q2 Marriage: Charles Napier McDonald & Annie Macdonald; Greenwich; 01D; 1159
1875 Q2 Birth: Edith Ann Mcdonald (mmn: Mcdonald); Wandsworth; 01D; 542
1877 Q1 Birth: Elizabeth Mcdonald (mmn: Mcdonald); Wandsworth; 01D; 608
1885 Q4 Birth: Florence Gertrude Mcdonald (mmn: Mcdonald); Lambeth; 01D; 467
1916 Q4 Death: Annie Robson Mcdonald; age 66 (born c1850); Christchurch; 02B; 988
1918 Q3 Death: Charles Napier Mcdonald; age 70 (born c1848); Christchurch; 02B; 808
Marriage
married: 11 May 1874; St Alphege, Greenwich
groom: Charles Napier? McDonald; fa; bach; Coach builder; King Street
bride: Annie? Macdonald; fa; spin; -; King Street
grooms father: John McDonald; station master
brides father: James Macdonald; distiller?
witnesses: Joseph Cherham?, Sophia Cherh__?
Baptism
name: Edith Ann McDonald
baptised: 07 Nov 1875; St John the Evangelist, Clapham, Lambeth
father: Charles Napier McDonald; coach maker
mother: Ann Robson McDonald
abode: 4 James? St
Probate
Charles Napier Mcdonald
of 63 Chatsworth Road Bournemouth
died 04 Jul 1918
Probate
to Frederick Charles Weaver, bank sub-manager
Effects £1249
https://probatesearch.service.gov.uk/Calendar?surname=mcdonald&yearOfDeath=1919&page=2#calendarCensus records:
1881 Gaskell Street, Clapham
Charles & Ann and daughters Edith & Elizabeth
Ref RG11; Piece 634; Folio 17; Page 25
https://www.familysearch.org/ark:/61903/1:1:Q27Q-PLQL1891 Cologne Road, Battersea
Charles & Ann and daughters Edith, Elizabeth & Florence
Ref RG12; Piece 436; Folio 18; Page 30
https://www.familysearch.org/ark:/61903/1:1:QZQQ-ZZM1901 Leigh Road, Eastleigh, Hampshire
Charles & Ann and daughter Florence
Ref RG13; Piece 1066; Folio 48; Page 31
https://www.familysearch.org/ark:/61903/1:1:XSFW-6BN1911 Leigh Road, Eastleigh, Hampshire
Charles & Ann and daughter Florence
https://www.familysearch.org/ark:/61903/1:1:XWQL-SQFNB: Check the image for the 1911 census as some transcripts have an obvious mistake