Might be no help but I put your query into ChatGPT and got these.
1. Thumbelina by Hans Christian Andersen
In this tale, Thumbelina is a tiny girl who experiences various adventures:
- She is left behind or separated from others.
- She seeks shelter in unconventional places.
- She is aided by animals, including a bird and a mouse.
These elements align with your mum’s memories of a fairy staying behind, setting up home in a lamp post, and interactions with birds and mice.
2. The Fairy Who Believed in Human Beings by Gertrude Alice Kay
This 1918 book tells the story of a fairy who stays behind when others leave, fascinated by humans. While it doesn’t mention a lamp post, the theme of a fairy remaining behind resonates with your mum’s recollection.
3. The Little Bookroom by Eleanor Farjeon
Published in 1955, this collection includes various fairy tales. While none match the description exactly, the stories often involve fairies, animals, and unique dwellings, which might be reminiscent of your mum’s memories.
4. Peg’s Fairy Book by Peg Maltby
This 1944 book features fairies and whimsical illustrations. While specific story details are scarce, the themes and imagery might align with your mum’s recollections.