What happened to your Florence Louise Adams in later life? Did she survive to appear in the 1939 Register, and if so does it confirm that her birthdate was 9 June 1871?
She married a George Staniforth in Portsmouth and then they moved to Hull. She died in 1942, but I can't find her in the 1939 Register.
But pretty confident that June 1971 in Camden is the right Florence. There were only a handful of Florence L Adams born around that time and she's the only one with a Wiltshire connection, and my grandmother and her sister both told me that's where their gran came from. I just wasn't convinced I'd pieced together her early years properly - and that's because I hadn't!
Thanks so much for everyone's help! I've spent months on this and you've cleared it up for me in less than 24 hours!