There are two births of Constance Bradford around 1883, one, who had Mary, in Wandsworth London and one, without Mary, in Wellington Shropshire.  So I used the 1891 see if a father named Robert Michael was in the house.  But none such found, so I cannot identify her birth in England (as stated at marriage in 1905).
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The GRO online index gives these Constances from 1880 to 1884:

Name:                             Mother's Maiden Surname:
   BRADFORD, CONSTANCE            TALBOT  
GRO Reference: 1882  S Quarter in WELLINGTON SALOP UNION  Volume 06A  Page 759
   BRADFORD, CONSTANCE ELSIE      MICHAEL  
GRO Reference: 1883  S Quarter in SWANSEA  Volume 11A  Page 707
   BRADFORD, CONSTANCE EMMIE      MOIST  
GRO Reference: 1881  S Quarter in RUGBY  Volume 06D  Page 527
   BRADFORD, CONSTANCE MARIE      SWIFT  
GRO Reference: 1883  D Quarter in TOXTETH PARK  Volume 08B  Page 249
   BRADFORD, CONSTANCE MARY       ROBERTS  
GRO Reference: 1882  M Quarter in WANDSWORTH  Volume 01D  Page 602
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The upshot is that, apart from her declaration in the “Duplicate Original” marriage certificate, that she was born in England, we have no evidence of that birth.
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Censuses might have some value:

The 1901 census has a Constance M Bradford aged 19 working as a ‘Mothers Help - Comfortic’ and born in Balham, London.  The family, of Taylors, were in Jettinhall, Staffords.  Balham merely happens to be rather close to Wandsworth, see above.
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Marriages might have some value:

this marriage was found in a wild search:

Surname   First name(s)        District  Vol  Page
Marriages Sep 1877   (>99%)
BRADFORD  Robert Michael       Stamford 7a   557
ROBERTS   Charlotte Elizabeth  Stamford 7a   557

So I looked in the 1881 census for them:

And there was this small family at Wandsworth:

First name(s)  Last name  Role  Marital status  Sex  Age  Birth year  Occupation  Birth place
Robert M     Bradford  Head  M  M  36  1845  Soap manufacturer  Rutland
Charlotte E  Bradford  Wife  M  F  24  1857  -                  Stamford, Lincolnshire
Andrew R     Bradford  Son   S  M   2  1879  -                  Rutland
Hugh M       Bradford  Son   S  M   1  1880  -                  Rutland
Elizabeth    Rignall   Serv  S  F  20  1861  Domestic servant   Alconbury, Huntingdonshire

And in 1891 there was:   Northing of them at all.  Might they have already gone to S. Africa?
But there were no Robert Bradford or their family on any boat to S Africa.

Bradford children born in England with a Roberts mother from 1877 were:

Name:                           Mother's Maiden Surname:
1. BRADFORD, ANDREW ROBERT         ROBERTS
GRO Reference: 1878  S Quarter in OAKHAM  Volume 07A  Page 324
2. BRADFORD, FREDERICK WILLIAM     ROBERTS
GRO Reference: 1879  M Quarter in ASHTON UNDER LYNE  Volume 08D  Page 548
3. BRADFORD, HUGH MICHAEL          ROBERTS
GRO Reference: 1879  D Quarter in OAKHAM  Volume 07A  Page 308
4. BRADFORD, GEORGE HERBERT        ROBERTS
GRO Reference: 1884  S Quarter in WANDSWORTH  Volume 01D  Page 584
5. BRADFORD, HERBERT               ROBERTS
GRO Reference: 1883  S Quarter in CHORLTON  Volume 08C  Page 691
6. BRADFORD, THOMAS ROBERTS        ROBERTS
GRO Reference: 1886  M Quarter in LAMBETH  Volume 01D  Page 486
7. BRADFORD, CONSTANCE MARY        ROBERTS
GRO Reference: 1882  M Quarter in WANDSWORTH  Volume 01D  Page 602

Of the above:
  1 and 3 were born in Oakham, Rutland where their parents had been married
     and were clearly in the 1881 census at Wandsworth in 1881.
  2 was born the same year at 3 and in a different place so eliminated.
  4 was born at Wandsworth in 1884 where the family had been lving at least since 1881
  7 Was born in Wandsworth in 1882 so the family might have stayed there.
  5 was born in Chorlton so not the Wandsworth family.
  6 could well have been the same family after a short move from Wandsworth;
     later he was proved to be a son by the data on his Death Notice

My conclusion is that, at last, I have located Constance Mary’s family and her birth in the first quarter of 1982.

It looks like they emigrated between 1886 and 1891; by 1891 they clearly were not in England.
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All the children of their parents were:

                                  Sources of information
                          <—-—- UK ———->                    SA
Birth                  Birth   1881   Death   <—-—-  Death Notices ———->
year   Forenames       Index  census  index   Father’s  Mother’s  Theirs   Marr
1878   Andrew Robert    1878    Y       N        N         N         -
1879   Hugh Michael     1879    Y      1917      NA        NA        -        
1882   Constance Mary   1882    NA               Y         Y       1948
1884   George Herbert   1884    NA               Y         Y       1956  
1886   Thomas Roberts   1886    NA               NA        NA      1909 (suicide)
1900   Philippa Gladys   NA     NA               Y         Y         N     1927=L W Stephens
1894   Edwin Herbert     NA     NA      NA       Y         Y       1966

Thomas Roberts’ Death Notice introduces a further sibling: Charles Frederick Bradford.

I cannot find a death record for Andrew Robert or Philippa Gladys.
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Her “Form of Information of a Death”:

1. Name:             Constance Mary Powys
2. Maiden name:      Bradford
3. Sex:              Female
4. Age:              66
5. Race:             European
6. Birth place:      England
7. Condition:        Widow
8. Occupation:       Household duties
9. Pensioner:        No
10. Death date:       Twentieth of January 1948
11. Death place:      Cato Road Nursing Home, Durban, Natal
12. Residence:        23 Crateford Court, Beres Road, Durban
13. Burial:           Crematorium, Stellawood Cemetery, Durban
14. Cause of death:   Carcinoma of rectum
15. Time of disease:  2 years
16. Doctor:           Dr K. M. Hainman
. . . .
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A note on her year of birth.  One or two urban myth reports have been made of her birth year and suggested it was in 1883 or 1884.  The evidence we have is:

  (a) At marriage in 1905 she said she was 23, giving a birth year of 1882.
  (b) At death, above she was reported in 1948 to be 66 years old, giving
      a birth year of 1882.
  (c) After establishing her birth family, above, her birth index says she
      was born in Q! of 1882.

So I have altered my record of her birth year to 1882.

And both at marriage and death she was said to have been born in England, so I have included just that.  Now detailed down to Wandsworth, Middlesex.

Finally I think the evidence is clear about her membership of this family:

1. The Bradford family started in Rutland with the marriage of Charlotte and Robert.
2. Two sons were born in Rutland before 1880
3. They then moved to Wandsworth and were shown in the 1881 census.
4. Constance Mary was born in Wandswarth as were George Herbert and Thomas Roberts.
5. The family was next found in South Africa with Constance, George and Thomas
   shown as children in the Death notices of both their parents.
6. Constance’s mother died at her hoe as it was recorded that Charlotte died
   at the home of her husband W O [Wilfred owen] Powys.
6. Philippa and Edwin were born in South Africa and shown as children on the death
   notices of their parents.

No more needs to be done: Constance was definitely a member of Charlotte and Robert Bradford’s family.
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Just found on the FamilySearch site a “Death Notice” for Constance Mary Sowys [ sic ].  I cannot really blame the transcribers for this as the ‘P’ is pretty like an ’S’ as well.  But when put beside the Death Notice of 1944 for her husband it is obvious from the content of this one that it is hers.  Details:

1. Name:          Constance Mary Powys born Bradford
2. Birth place:   England
3, Parents:       Both deceased
4. Age:           65 years   [ Ho Ho! see above]
5. Occupation:    widow
6. Residence:     23 Crateford Court, Bere Road, Durban
7. Condition:     Widow
    Husband:       Wilfred Owen Powys died about 1944 in Durban leaving all to his widow
    Marr. Place:   Transvaal, Germiston
8. Death date:    20th January 1948
9. Death place:   Cato Road Nursing Home, Durban
10. Children:      Horace Victor Powys
                   Marjory Gladys Collier wife of Cecil Collier
                   both adults
13. Effects        Estimated to be above £300.

Dated at Durban on 28th day of January 1948
Signed by:         H V Powys, son of deceased, sansbody(?) of deceased
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Their marriage at last found on FamilySearch, with image; transcript by me:

>               St Boniface, Germiston, Transvaal  >  1896-1918

“                         Page 50
“MARRIAGES solemnized at St Bonifac Church, in the Parish of Germiston
“   in the Year 1905
“No:
“When Married:
“Bann/Licence:  Banns

                 His                 Hers
                 ===                 ====
“Name:        Wilfred Owen Powys  Constance Mary Bradford
“Age:         34                  23
“Birthplace:  Natal               England                       *
“Condition:   Bachelor            Spinster
“Contract     With ante-nuptial   With ante-nuptial contract    *
“Profession:  Stockeeper          -
“Residence:   Germiston           Germiston
“Consent:     Own                 Own

“Married in S. Boniface Church Germiston by me, E J Dyson, Rector

“This marriage was solemnized between us …  W.O.Powys,  C. M. Bradford
“   in the presence of:  R.M. Bradford, C.J. Bradford

*  The two lines only appear on the Marriage certificate labelled “Duplicate Original”
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