The mystery deepens . . .
I now have the death certificate for “M” (I won’t use her full name while her sister is still living) which shows her DOB in October 1917. I’ve looked again at the birth registration and there are two:
Stafford RD Q1 1935 vol 6B page 29, mmn “L”
Stafford RD Q4 1917 vol 6B, no page number, mmn “L”
On the original index for Oct-Nov 1917 there is a handwritten entry for “M” with her mmn, RD, volume and a comment “see M ’35”.
I think there is little doubt that both entries refer to the same person.
“M”s mother was born in Q4 1903 and married in Q3 1919 – age just about 16. On the basis that the 1917 birth date is correct, “M” was born when her mother was only 14. There is a GRO birth record for “M”, surname “L” (as mmn), for Stafford RD Q4 1917 with the comment “Occasional copy: A”.
This resolves the original query about the YOB on the GRO index for deaths - which is correct at 1917 - but quite why she has two birth registrations is still a puzzle, as is the fact that my mother believed the 1935 date to be correct.