and Jane, born 1875 and last sighted with her mother and her sister Marion in lodgings in Bath.
You said Marion Gordon Black was born in 1884
A free search of the 1939 register for Marion G Black, born 1884 brings up a result in Hexham, the other person in the household is a Jane Black.
Unfortunately a free search for Jane Black, in Hexham brings up a person born in 1924 in the same house as Marion G Black .
We aren't allowed to do look ups on the 1939 register but if you have access I'd recommend you look at the image to check the transcription of Jane's birth year.
Bearing in mind a 7 is often mistaken for a 2 and the year was recorded as two digits only, so if it had been read as 2 then it would make sense for it to be typed as 1924.
Even with the apparent discrepancy of the birth year for Jane, I'd put this record in the 'possible' category, certainly worth looking at further anyway.
Especially as the probate calendar for 1955 has an entry for
BLACK Marion Gordon of Dale House, Farnley, Corbridge, Northumberland, spinster died 18 August 1855 Probate* Newcastle upon Tyne 6 December to Ian Desmond Landells Black commercial traveller and Gavin Black marine surveyor Effects £5211 2s 8d
(* Probate indicates she left a will)
and the probate calendar for 1948 has an entry for
BLACK Jane of Craigie Allendale Road Hexham Northumberland, spinster died 21 June 1948 Administration Newcastle upon Tyne 10 September to Marion Gordon Black spinster Effects £4033 6s
(*Administration indicates she did not leave a will)
Probate calendar entries are viewable for free here
https://probatesearch.service.gov.uk/#wills he he always best to see for yourself as I can produce typos as well as anyone else!
Free BMD has a death Reg for a Jane Black Q2 1948, Northumberland W, age 73 which is consistent with your Jane's birth year and makes the 1939 register entry a lot more likely.
Addedand that 1939 entry is even more likely now. After I found their Mam's probate and it said she'd lived at Tynedale Terrace, Hexham I did a free advanced search on the 1939 register for Tynedale Terrace in Hexham. Two of the people recorded as living there were Marion G Black and Jane Black.
I do like it when things work out neatly :-), though please check it all out carefully, its still just my opinion and you need to check and decide for yourself.
Boo