There are two Elizabeth Myers births on FreeBMD b. in 1912, one in Hemsworth, W Yorks and the other in Tynemouth, Northumberland.  Which might be her?  1921 census?

Not the cheap way.  Start here:

(a) The probate Office index says she died in 1947 at The Quarry House, Sherborne, Dorset

(b) Her death index, the only death in Dorset:

Name:                   Age at Death (in years):  
POWYS, ELIZABETH        34  
GRO Reference: 1947  J Quarter in STURMINSTER  Volume 06A  Page 557

So she was born c. 1913.  I have been told that she was in fact born in 1912, but this needs confirmation.

(c) In 1939 there were 13 Elizabeth Myers who were born in 1912±2.

(d) I think I will have the same trouble with the 1921 census

(e) the only, expensive way of narrowing her birth down is to get her father’s name, as found on her marriage certificate.
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On a passenger list for a boat trip to New York in 1946 she was 34 years old, living at the Quarry House Sherborne and an Author.  On the return trip she was still 34 but no mention of being an author.
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March 2022, TFPL: Her marriage certificate is here and gives her father’s name as George William Myers and her age as 30 in 1943.  So she was born in 1913, already known as above.  An Eleanor Myers signed as a witness, her mother?

There are 11 George William Myers who got married from 1888 to 1910.  If his wife was Eleanor, this brings it down to one marriages, in Barton Regis, Glos in 1888 but this was to an Ellen Davies.

There were 230 Georege William Myers in the 1911 census.  Absolutely hopeless!

The only answer now is to look her up in the 1921 census.  There are three results for an Elizabeth Myers born around 1913 and the house also including a George William.  And I don’t want to buy all of these.

I paid for the most likely one, having an Elizabeth whose birth was as near to 1912 as possible and got this record: from an enormous family of Myers of children and nephews. nieces and brothers of the widow who was head of house:

Name:         Elizabeth Myers
Rel to hear:  Niece
Age:          8 years, 11 months
Parentage:    Mother dead
Birth place:  St George’s London
Schooling:    Full-time

This Elizabeth’s birth would have been 1812 around April.  But I am not convinced this is the right Elizabeth.  
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But the investigations did lead to finding an Elizabeth Myers in the 1939 Register with the addition of a later change of name on the form to Powys and thus must be this Elizabeth.  She was at Grove Park Hospital, Lewisham (patients, etc).  The data for her was:

                                            Cond-                 Schedule
ForeName   Surname  Birth date  Sex  Role   ition   Occupation    Main  Sub
Elizabeth  Myers    23 Dec 1912  F     P      S     Waitress       14   125
  where Role of ‘P’ seems to mean Patient.

Ref:      1939 ref: RG101, piece 0385D, Item 11. line 29
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This brings her a bit closer.  As she was born just over a week from the end of 1912, she would have had her birth registered either in Q4 of 1912 or Q1 of 1913.

This is the list of all Elizabeth Myers birth registrations in 1912 and 1913:

Name:                       Mother's Maiden Surname:
MYERS, ELIZABETH HELEN      DEAN  
GRO Reference: 1912  M Quarter in HEMSWORTH  Volume 09C  Page 379
MYERS, ELIZABETHETTA        BULLOCK  
GRO Reference: 1912  S Quarter in TYNEMOUTH  Volume 10B  Page 391 MYERS, ELIZABETH            HICKEY  
GRO Reference: 1913  M Quarter in MANCHESTER  Volume 08D  Page 466
MYERS, ELIZABETH            BRADLEY  
GRO Reference: 1913  J Quarter in DURHAM  Volume 10A  Page 825
MYERS, ELIZABETH ANN        ROSE  
GRO Reference: 1913  S Quarter in MILE END OLD TOWN  Volume 01C  Page 653
MYERS, ELIZABETH            SMART  
GRO Reference: 1913  S Quarter in WEARDALE  Volume 10A  Page 642
MYERS, ELIZABETH            SCHOFIELD  
GRO Reference: 1913  D Quarter in ROTHERHAM  Volume 09C  Page 1628

The above shows no birth registrations in Q4 of 1912 and but one in Q1 of 1913.  So she was born in Manchester.  Her mother’s maiden name was HICKEY.  BUT no marriage can be found for a George William Myers to a N.N. Hickey.
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Her probate index:

1947
POWYS ELizabeth Myers of The Quarry House Sherborne Dorsetshire (wife of Littleton Charles Powys) died 24 May 1947  Administration Bristol 29 August to the said Littleton Charles Powys retired schoolmaster.  Effects £729 12s. 1d.
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Their marriage:

Surname   First name(s)   Spouse   District   Vol   Page
Marriages Dec 1943   (>99%)
Myers     Elizabeth       Powys    Hampstead  1a    1128  
Powys     Littleton C     Myers    Hampstead  1a    1128
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I had to obtain her marriage certificate to identify her father:

“1943. Marriage solemnized at St Mary’s Chapel in the
“  District of Hampstead in the Metropolitan borough of Hamptead
No;            191
When Married:  Seventh October 1943

                  His                               Hers
                  ===                               ====
Name:          Littleton Charles Powys           Elizabeth Myers
Age:           69 years                          30 years
Condition:     Widower                           Spinster
Profession:    School master (retired)           Author
Residence:     Priestland Cottage, Sherborne     12 Carlingour Road, N.W.3.
Father:        Charles Francis Powys (deceased)  George William Myers (deceased)
Father’s job:  Clerk in Holy Orders              Independent means

“Married in the St Mary’s Chapel according to the Rites and Ceremonies
“  of the Roman Catholics by Licence by me, M Gomes, Priest; Eng M. Fawcett, Deputy Registrar

“This Marriage was solemnized between us, Littleton C Powys, Elizabeth Myers
“  in the Presence of us, Eleanor Myers, Oliver Hoe
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