Terry,
"1939 Register, Workington
Rodgers Blanche DOB 30 Dec 1909 (and there is another notation in lighter pen/pencil 21.10.50 that I don’t understand)"

Here are the meanings of the later entries. Note that the address in 1939 was in enumerator area HBKX

Whoever gave the info to the enumerator in September 1939 could have made mistakes in birth dates
The pencil additions on 21/10/50 for Blanche are to show that she has reported that she is at a new address (in area HBD). At the same time there is a pencil note to say the birth date should be 26 12 1910. So the 1939 Register contains info that indicates that Blanche may have been born 26th Dec rather than 30th Dec.
There is also a pencil note alongside daughter Margaret dated 17/10/1950 to say that she has moved to a new address in area HBD.
Margaret also has a note in Green saying her birthday was 17/11/1938, This green note is clearly referring to this death in Q4 1983
RODGERS MARGARET 17NO1938 WHITEHAVEN 1 691

Coincidentally it looks like Margaret's twin sister Eileen married a man called Storey and when she died her birth was reported as 1938 not 1939
STOREY, EILEEN 1938
GRO Reference: DOR Q4/2009 in COCKERMOUTH (3761A) Reg 1A002 Entry Number 502459336

I do not know who reported Blanche's birthday on her death registration but I do know it was not Blanche herself, and it was not John her husband (and apparently not Margaret the daughter).
I wonder if the births of twins Margaret and Eileen were a case of very late registration and a false (later) birthday was reported to avoid the fines!
Dave