I did a tree for a friend who is an Arkinstall. Her father was William b. 1917. Phyllis L.M was his younger sister.
I couldn't get any further with mother Phyllis so concentrated on the Arkinstall's which faired a lot better.
I'm not sure if mother Phyllis was quite telling the truth about her father.
If memory serves she said on her marriage she was a lady dentist & her father was called Alfred.
Thanks to those on this thread she appears to be the daughter of Maria Lee nee Brookes. On the census Maria is described variously as being married widowed married again & widowed again but always had the name Lee. She was never with any husband on any of them. They lived in Dudley.
Although this was for a friend it might be worth another visit now you've peaked my interest.
This from an earlier post:
School registers for Park School (Girls'), Dudley, show a Phyllis Lee born 9 Oct 1885, address 36 Stafford Street, father Samuel Date of Admission: 31 Mar 1896, Date of leaving: 11 Mar 1898. Previous school was Wolverhampton St Girls.
I still can't be sure I'm looking for a Phyllis born 1885 or 1891.