His birth:

Surname First name(s) District Vol Page
Births Dec 1873   (>99%)
HAWKSLEY Robert Edward W Taunton 5c 361
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This looks like him in 1901:

Name Relation Condition Sex Age Birth Year Occupation   Disability  Where Born

HAWKSLEY, Warren Boarder Single M 27 1874 Architect & Surveyor  Taunton, Somersetshire

RG number: RG13 Piece: 2918 Folio: 14 Page: 19    

Registration District: Rugby Sub District: Rugby EnumerationDistrict: 27
Ecclesiastical Parish: St Matthews

Civil Parish: Rugby Municipal Borough:
Address: 23, Pennyton Street, Rugby
County: Warwickshire
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I think the 1901 entry is confirmed by this of 1911 when he was married and with 2 children.  They reported that they had had 2 children, both of whom were living.

Name Relation Condition/ Yrs married Sex Age Birth Year  Occupation  Where Born

HAWKSLEY, Robert Edward Warren Head Married M 37 1874  Architect And Surveyor  Somerset, Taunton
HAWKSLEY, Lilian Mary Wife Married 9 years F 33 1878   Warwickshrie Rugby
HAWKSLEY, Phyllis Lilian Daughter F 8 1903 Warwickshrie Rugby
HAWKSLEY, Warren Bradshaw Son M 3 1908 Warwickshrie Rugby
DUTHAM, Edith Mary Servant Single F 24 1887 General Servant Domestic Warwickshrie, Rugby

RG number: RG14 Piece: 18598 Reference: RG14PN18598 RG78PN1112 RD391 SD1 ED13 SN112

Registration District: Rugby Sub District: Rugby EnumerationDistrict: 13
Parish: Rugby

Address: 30 Dunchurch Road Rugby
County: Warwickshire
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FreeBMD shows them to have had no more children and no death for him before c. 1935.

Their marriage:

Surname First name(s) District Vol Page
Marriages Dec 1901   (>99%)
HAWKSLEY Robert Edward W Rugby 6d 1076
Bradshaw Lilian Mary Rugby 6d 1076