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That explains the confusion - middle name Hinton (not Winton)

Elsie is boarding with the Georges and birthplace is given as Winchester Union which suggests the workhouse infirmary. Think you'll need to buy her birth cert to find out who her parents are.

There are birth registers which cover that year in hampshire record office but their charge is dearer than buying the cert (unless you live near enough to visit yourself).

In 1911, Percy Rideout is STEPSON

1901


Name: George Gray
Age: 42
Estimated Birth Year: abt 1859
Relation: Head
Spouse's Name: Bessie Gray
Gender: Male
Where born: Shaftesbury, Dorset, England
Civil parish: Shaftesbury
Ecclesiastical parish: Shaftesbury St James
Town: Shaftesbury
County/Island: Wiltshire
Country: England



Registration district: Shaftesbury
Sub-registration district: Shaftesbury
ED, institution, or vessel: 7
Neighbors: View others on page
Household schedule number: 73
Piece: 1965
Folio: 48
Page Number: 11
Household Members:
Name Age
George Gray 42
Bessie Gray 33
Percy Gray 15
Maggie Gray 12
Stanley Gray 7
William Gray 5
Gertrude Gray 10 Months

Name: Bessie J Rideout
Age: 22
Estimated Birth Year: abt 1869
Relation: Niece
Gender: Female
Where born: Gillingham, Dorset, England
Civil parish: Gillingham
Ecclesiastical parish: Gillingham
Town: Gillingham
County/Island: Dorset
Country: England

Registration district: Shaftesbury
Sub-registration district: Gillingham
ED, institution, or vessel: 4
Neighbors: View others on page
Piece: 1630
Folio: 29
Page Number: 4
Household Members:
Name Age
Grace Rideout 76
George Bealing 81
Bessie J Rideout 22

Percy had been put in the Workhouse in 1891


Dorset, England, Births and Baptisms, 1813-1906
Name: Percy Rideout
Baptism Date: 20 Jul 1886
Parish: Fontmell Magna
Mother's Name: Elizabeth Jane Rideout

England & Wales Christening Records, 1530-1906
Name: Elizabeth Jane Rideout
Gender: Female
Christening Date: 20 Oct 1867
Christening Place: West Orchard, Dorset, England
Father's Name: John Rideout
Mother's Name: Jane

1891

Name: George Gray
Age: 30
Estimated Birth Year: abt 1861
Relation: Son
Father's Name: George Gray
Mother's Name: Hannah Gray
Gender: Male
Where born: Shaftesbury, Dorset, England
Civil parish: St James
Ecclesiastical parish: St James
Town: Shaftesbury
County/Island: Dorset
Country: England

Registration district: Shaftesbury
Sub-registration district: Shaftesbury
ED, institution, or vessel: 5
Neighbors: View others on page
Piece: 1628
Folio: 52
Page Number: 13
Household Members:
Name Age
George Gray 54
Hannah Gray 52
George Gray 30
Alfred Gray 26
Margaret Gray 21
Gertrude Gray 15
Beatrice Gray 10/12

Dorset, England, Marriages and Banns, 1813-1921
Name: George Gray
Birth Year: abt 1865
Age: 27
Marriage or Bann Date: 26 Dec 1892
Parish: Fontmell Magna
Father's Name: George Gray
Spouse's Name: Elizabeth Jane Rideout
Spouse's Father's Name: John Rideout

It isn't surprising that Cynthia knew nothing of her mother's family.........the 1911 census indicates that Elsie wasn't brought up by her own family.

The evidence suggests that she was born to an unmarried female named Ball...............the second name Hinton possibly being a clue as to the father's identity.........

You really will have to purchase Elsie's birth cert if you wish to make any sort of progress on her line........and even then, it may not prove exactly easy.