Florence seems quite elusive - I have found her in 1911 (but cannot post details on here for copyright reasons). No sign of her in 1901 or 1891.
There is a Florence M White b 1886 and a Charles (Eli) White in the same household in Beaminster district on the 1939 register. No year of birth is listed for Charles on the free preview. I'm not sure why Eli is in brackets after Charles's name.
That would match with a birth registered Q4 1886 in Bridport district for Florence M Huxford.
I don't know whether this connects at all but there is a marriage of a George Huxford to Ann Brown in 1869. In 1871, Ann is living with her parents (John and Mary Brown) and there is a 2 month old baby Ida Letitia Brown in the household. In 1881, Ann is still with her parents, Ida is 10 and listed as Ida Huxford and there are two other Huxford children Fanny and Lucy, but still no sign of Ann's husband.
This family also seems to disappear in 1891 and 1901. I think the child Lucy may marry in 1902 in Axminster district and it looks like her husband might be James White
Ida Letitia Huxford married John Rowe at Monkton Wyld on 21 june 1893, record on Dorset OPC confirms her father is George Huxford occ gardener.
Curiously there is a married George Huxford, occupation also gardener on 1871 and 1891 censuses, married but no wife with him and with children whose birth predate the marriage between a George Huxford and Ann Brown. His year of birth is abt 1829 so quite a bit older than Ann (b abt 1849).
In 1901 Ida Rowe and children are visiting the Wareham family in Hawkchurch. That is James Wareham age 47, Ann Wareham (b abt 1849), and Wareham children including a Florence b abt 1886 and a Lucy b about 1881 - seems like a lot of coincidences here.