Her birth:

Surname   First name(s)      District   Vol  Page
Births Dec 1876   (>99%)
VAUGHAN Ivy Clelia G Winchester 2c 97
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Not found in 1901 census, not even with no surname and just the county of her birth.
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In 1911 census they had one son and had been married for thirteen years and were living in a 15 roomed house with 5 live-in servants.  She said she had had two children, one of whom had died:

  Marriage  Years               Birth
Surname  Forename  Age  Gender  Relation   Status   Married  Occupation Place

Halsey Bircham Bernard Edward 42 Male Head  Married  13  Solicitor London
Halsey Bircham Ivy Clelia 34 Female Wife Married  13  Winchester, -  
Halsey Bircham Arthur Christopher 3 Male Son  Single - Worplesdon, Surrey
Tucker Beatrice Annie 27 Female Servant Single - Nurse Axminster, Devon
Thompson Sarah Ann 28 Female Servant Single - Parlourmaid Edith Weston, Rutland
Prior Sarah Gregory 40 Female Servant Single - Cook Benstead, Hampshire
Watts Annie Eliza 23 Female Servant Single - Housemaid Yorkley, Gloucestershire
Gower Grace Emily 20 Female Servant Single - Housemaid Scaynes Hill, Sussex

Ref: RG14 - PN3045 RD33 SD1 ED18 SN49

Address: Admirals Walk, Pirbright, Surrey
Registration District: Guildford
Sub District: Woking
Civil Parish: Pirbright
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This looks very strongly like their first child:

Surname   First name(s)      District   Vol  Page

Births Dec 1906   (>99%)
Bircham Francis Powys    Guildford 2a 71

And his infant death:

Surname   First name(s)   Age   District   Vol  Page
Deaths Mar 1907   (>99%)
BIRCHAM Francis Powys H 0 Guildford 2a 74
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No further births found after 1911.
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Her death:

Surname   First name(s)   Age   District   Vol  Page
Deaths Jun 1942   (>99%)
BIRCHAM Ivy C G H 74 Mere 7c 431
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Their marriage:

Surname   First name(s)      District   Vol  Page
Marriages Dec 1897   (>99%)
BIRCHAM Bernard Edward H Chelsea 1a 784
Vaughan Ivy Clelia G    Chelsea 1a 784