I couldn't find any information in poll books before 1947 so I would guess that's when Florence first appeared on the scene.

Florence ACHESON - date of birth: 13 March 1910

ANCESTRY - Probate

Florence ACHESON, 44 Larchwood Drive, Gloucester
died 9 January 1973
Probate: Oxford - 25 January
£33,626

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British Phone Books

1972

F Acheson

44 Larchwood Dvjuffley (Dv, Tuffley)

Telephone No: Gloucester : 31335

Gloucester

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Also - any connection?

ACHESON J F H East Wv, South Fm : Telephone : Burbage 287

Here's the full notice from the Birmingham Daily Post - Monday 07 December 1964

Dr. Leslie Batten Currie Trotter. of Stroud Road, Gloucester, a well-known member of a medical family in the Forest of Dean, and for many years in practice at Ledbury, left £40,548 (£40,432 net). Duty of £11,329 has been paid. His bequests included "all my collection of dried mosses in their cabinets together with the cabinets" to the National Museum of Wales. The Herbarium, Cardiff: £1,000 to the Linnean Society and "the original work by Professor Joseph Else and myself entitled Histology of British Mosses contained in two large deed boxes: £l,000 to the British Bryological Society and "my bryological literature and library to be disposed of to members of the society or retained by the society as the executive of the society thinks best." £500 to Dr. Barnardo's Homes.

Leslie Trotter is listed at the same address at the same time.

I wonder if a query like this will be better served by writing an open letter to be printed in the local newspapers, and hopefully their readers will know something ?.

Searching the BNA online newspaper archives may help, chances are the report on Dr L.B.C. Trotter's funeral in 1964 may mention her as well ?.
Having said that, the coverage of local papers such as the Gloster Citizen only covers upto 1950, and the Hereford Times a lot earlier than that. If you're able to visit Cinderford Library they have the Dean Forest Mercury on microfilm.

I don't currently have a subscription so cannot give the full article, but the BNA site's search engine does give the following,

"Dr. Leslie Batten Currie Trotter. of Stroud Road, Gloucester, a well-known member of a medical family in the Forest of Dean, and for many years in practice at Ledbury, left R 40,548 (RA0,432 net). Duty of £11,329 has been paid. His ..."

Published: Monday 7 December 1964
Newspaper: Birmingham Daily Post

https://www.britishnewspaperarchive.co.uk/

Dr LBC Trotter and his home in Ledbury gets a mention and photos here.
http://www.old-ledbury.co.uk/Streets/RosswayNewStreet.htm

He was educated at Cambridge, and served in the RAMC in France in WW1;

"LESLIE BATTEN CURRIE TROTTER (born 1882). M.A., M.D., B.Ch. (Cantab.).
Leslie Batten Currie Trotter (born 1882) [Epsom College 1898-1901] was the son of Dr L. B. Trotter, of Coleford, Gloucestershire. He received his medical education at Clare College, Cambridge and University College Hospital, before entering general practice at Ledbury, Herefordshire. During the First World War he served as a Captain in the R.A.M.C., at Ypres and in Italy (1914-1918)."
http://atelim.com/epsom-college-1855-1899-general-practitioners-medical-officers.html?p...

Sadly I'm unable to find his Medal Card etc.

He is mentioned in the following downloadable document, as follows;

"Leslie Batten Currie Trotter (1882-1964)

Member: ?1921-1964
Bryological activity:
Herbarium:

Trotter was born at Coleford, Gloucestershire, a son of Dr. Leslie Batten Trotter (c.1850-1934) and Elizabeth (née Currie, 1858-1882). Leslie Trotter senior was a son of Thomas Birt Trotter (1806-c.1855), grocer and general merchant at Coleford, and Jane (née Thomas, c.1815-1885). Elizabeth Currie was a daughter and fifth child of John Currie (1814-1904), chemist and druggist of Glasgow, and Mary Stark (née Kirkwood, 1823-1901). John Currie was a son of John Currie, a candlemaker, and Elizabeth (née Kirkwood). Mary Kirkwood was a daughter of Robert Kirkwood (born c.1784), a house factor in 1851, and Jean or Jane (née Stark, c.1782).

Leslie Trotter senior married secondly Elizabeth Mary Catchpole in 1890.

Trotter’s first cousin, Wilfred Batten Lewis Trotter (1872-1939) was surgeon to the King, Professor of surgery at University College Hospital in London, and also wrote The Instincts of the Herd in Peace and War (1914); he has an entry in the Dictionary of National Biography.

Leslie Trotter practised as a physician in Ledbury from 1913 until 1939, and joined the MEC in 1921, becoming President of the BBS in 1956. In 1914 he married Hilda Mary (née Pierce), daughter of John Pierce, solicitor of Nottingham, and Hannah Louisa (née Bullock). Hilda was drowned in a boating accident off the coast of the West Highlands in 1943, along with Cecil Marquand (q.v.).

Trotter’s plants are at the National Museum and Gallery of Wales in Cardiff, and his drawings are at the Linnaean Society in London."

https://rbg-web2.rbge.org.uk/bbs/Learning/Bryohistory/MEC_BBS%20Members.rtf

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From Familysearch;

1891 Census; Coalway Road, St John's Parish, Monmouthshire.
Household Role Gender Age Birthplace
Leslie B Trotter Head M 40 Married. Doctor of Medicine. Gloucestershire, England
Mary Trotter Wife F 40 Married. Herefordshire, England
Leslie B C Trotter Son M 8 Scholar. Gloucestershire, England
Wilfred B L Trotter Nephew M 18 Unmarried. Student of science. Gloucestershire, England
Frances Trotter Niece F 24 Unmarried. Australia
Alice Morgan Servant F 28 Unmarried. Domestic cook. Clearwell, Gloucestershire, England
Emily Willis Servant F 15 Unmarried. Domestic Servant. Gloucestershire, England

Name Leslie Batten Courie Trotter
Event Type Census
Event Date 31 Mar 1901
Event Place Epsom, Surrey, England
County Surrey
Civil Parish Epsom
Ecclesiastical Parish St Martins
Sub-District Epsom
Registration District Epsom
Gender Male
Age 18
Occupation STU
Relationship to Head of Household Pupil
Birth Year (Estimated) 1883
Birthplace Newland, Gloucestershire
Page Number 5

Name Leslie Batten Currie Trotter
Alias BATTEN CURRIE
Event Type Census
Event Date 1911
Event Place Islington, Upper Holloway N, London, England
County London
Parish Islington
Sub-District Upper Holloway
Sub-District Number 2
District Number 10
Enumeration District 24
Registration District Islington
Gender Male
Age 28
Marital Status SINGLE
Marital Status SINGLE
Occupation MEDICAL PRACTITIONER
Industry GENERAL HOSPITAL
Institution GREAT NORTHERN CENTRAL HOSPITAL
Birth Year (Estimated) 1883
Birthplace Coleford, Gloucestershire
Relationship to Head of Household Medical Officer
Schedule Type 1
Page Number 1
Registration Number RG14
Piece/Folio 183
Affiliate Record Identifier GBC/1911/RG14/00820/0183/5

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Name Florence Acheson
Event Type Birth
Event Date Apr - Jun 1910
Event Place Cavan, Ireland
Registration Quarter and Year Apr - Jun 1910
Registration District Cavan
Volume Number 3

1911 Ballintemple, County Cavan, Ireland
Household Role Sex Age Birthplace
Thomas S Acheson Head of Family M 46 Farmer. Co Cavan
Martha Acheson Wife F 32 Co Cavan
Wm Francis Acheson Son M 7 Co Cavan
Florrie Acheson Daughter F 1 Co Cavan
Thomas Acheson Uncle M 78 Retired farmer.

Have you looked-up Florence in the 1939 Register ?.

Surname First name(s) Mother/Spouse/DoB District Vol Page
Deaths Mar 1973 (>99%)
ACHESON FLORENCE 13MR1910 GLOUCESTER C 7B 1217

Sadly that's the only record I can find that def relates to her. Was Acheson her maiden name or had she married as I suspect ?.

Maybe worth searching the old newspapers ?

PS Seems she never married so had no descendants, a general internet search find this mention in the London Gazette. When she died she was living in Gloucester.

see https://www.thegazette.co.uk/London/issue/45901/supplement/1892/data.pdf

Re Doctor Trotter, could he have been Leslie, son of this Doctor Trotter in this old thread ?.
https://forum.forest-of-dean.net/index.php?id=47937