His probable birth:

Surname First name(s) District Vol Page
Births Dec 1847   (>99%)
SHARPE William Arthur Islington 3 235
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Two William Arthur marriages and my bet is on the first but no idea of the wife:

Surname First name(s) District Vol Page
Marriages Sep 1875   (>99%)
HILHOUSE Harriette Kate Lambeth 1d 798   
Lawford Mary Evelyn Lambeth 1d 798   
PRESTON Harry William Lambeth 1d 798   
Sharpe William Arthur Lambeth 1d 798

Marriages Dec 1878   (>99%)
DAVY Hannah Stockton 10a 79   
SANDERSON Thomas Stockton 10a 79   
Scott Mary Jane Stockton 10a 79   
Sharpe William Arthur Stockton 10a 79

And from the 1881 census, below, he must have married Mary Evelyn Lawford.
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In the 1881 cesnsus this is the only William A Sharpe, solicitor born in Middlesex, so has to be him:

Name Relation Condition Sex Age Birth Year Occupation  Disability  Where Born

SHARPE, William A Head Married M 33 1848 Solicitor  Highbury, Middlesex
SHARPE, Mary E Wife Married F 27 1854   Highgate, Middlesex
SHARPE, Francis E Daughter Single F 4 1877   St Pancras, Middlesex
SHARPE, Eleanor Daughter Single F 3 1878   St Pancras, Middlesex
CHAMBERLAIN, Sarah Servant Single F 20 1861 Nursemaid (Domestic)  Islington, Middlesex
KNOTTS, Harriett Servant Single F 23 1858 Housemaid (Domestic)  St Pancras, Middlesex
ROWLING, Eliza A Servant Single F 22 1859 Cook (Domestic)  Great Wenham, Suffolk

RG number: RG11 Piece: 220   Folio: 99 Page: 75    

Registration District: Pancras Sub District: Kentish Town
EnumerationDistrict:  Ecclesiastical Parish:

Civil Parish: St Pancras Municipal Borough:
Address: 12, St Albans Villas, St Pancras
County: Middlesex
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In 1891 he had four more children plus his wife’s sister Florence Lawford (confirming his wife’s maiden name) in the house and four servants. Charles was said to be 19 but in fact was ten years younger. He was now in Highgate, Mx:

Name Relation Condition Sex Age Birth Year Occupation  Disability  Where Born

SHARPE, William A Head Married M 43 1848 Solicitor  Islington, Middlesex
SHARPE, Mary E Wife Married F 37 1854   Hornsey, Middlesex
SHARPE, Frances E Daughter Single F 14 1877 Scholar  St Pancras, Middlesex
SHARPE, Eleanor Daughter Single F 13 1878 Scholar  St Pancras, Middlesex
SHARPE, Charles A Son Single M 9 1882 Scholar  St Pancras, Middlesex
SHARPE, Philip H Son Single M 7 1884 Scholar  St Pancras, Middlesex
SHARPE, Reginald L Son Single M 4 1887    Islington, Middlesex
SHARPE, Catharine Daughter F 1 1890    Hornsey, Middlesex
LAWFORD, Florence Sister In Law Single F 19 1872 Scholar  Wandsworth, Surrey
THOMPSON, Mary E Servant Single F 48 1843 Nurse  Lancaster, Lancashire
PENNING, Eliza A Servant Single F 36 1855 Cook  Saffron Walden, Essex
SOTHERTON, Ethel M Servant Single F 23 1868 Housemaid  Arley, Staffordshire
WADDS, Catherine M Servant Single F 16 1875 Nurse Maid  Hornsey, Middlesex

RG number: RG12 Piece: 1061 Folio: 104 Page: 68    

Registration District: Edmonton Sub District: Hornsey
EnumerationDistrict: 11 Ecclesiastical Parish: All Saints

Civil Parish: Hornsey   Municipal Borough:
Address: 4, Broadlands Road, Hornsey, Highgate
County: Middlesex
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In 1901 all children were at home plus the last child, George, who had been born in 1893:

Name Relation Condition Sex Age Birth Year Occupation  Disability  Where Born
SHARPE, George R Son Single M 8 1893   Islington, Middlesex

RG number: RG13 Piece: 1244 Folio: 37 Page: 3
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In 1911 he was a widower but with a son William Seaford Sharpe who was not in any previous census, aged 31, born in Seaford, Sussex and a solicitor.  Where had he come from?

Their marriage:

Surname First name(s) District Vol Page
Marriages Sep 1875   (>99%)
Lawford Mary Evelyn Lambeth 1d 798   
Sharpe William Arthur Lambeth 1d 798