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i don't have his service record.  The date of enlistment came from his Silver Wound Badge record as 10/09/1909 discharged 06/08/1919.  He would have been 17 on enlistment.  Haven't found Alice in census returns.
From another site picked up that Hope Street, Glasgow was some form of pre registrars office or solicitors office that officially recognised a marriage via a Warrant of Sheriffs Substitute. 
I therefore, surmise he possibly didn't have formal permission to marry as he was in the army and gave the Bricklayers Labourer to cover for being a soldier.  As the outbreak of war was likely he probably wanted a formal record of marriage as two children had already been born in the event of his death in service.  The other site referred to a Scots Guardsman in London and a maid travelling to Hope Street in similar circumstances.

Boo,

Thank you for your time, searches and information.  That has been helpful. 

I have also found this site https://www.gatesheadpolicehistory.org/history.  It has the Force Registers for Gateshead Police Force between 1836 to 1899 and men and women between 1900 to 1968.

Unfortunately the 1900 to 1968 register is a work in progress, last updated in 2021.

Just bringing this to the front again.  Haven't been able to break down the brick wall on this one.  Just posting again if there are any new sources available that I may have overlooked or not be aware of.

The only record I have found since, is his attempt to enlist in the Royal Irish Fusiliers in 1906, when he was clearly underage by a year, give is birth date as 1889 and later was discharged.  He used only William Walker on enlistment. 

Details of Militia Attestation Papers, 1800-1915:- William Walker, Gender Male, Marital Status Single, Age 17, Birth Year abt 1889, Birth Place Tullylish, Gilford, Down, Ireland, Enlistment Date 5 Nov 1906, Enlistment Place Portadown, Ireland, Regiment 87th Foot (R. Irish Fusiliers), Service Number 4782, Father James Walker, Mother Jane Eliza.

Some further details:  They do not hold employee registers but do hold the following records that may be of interest:

U95- Records of the Glenboig Union Fireclay Co Ltd, brick manufacturers, Glenboig, 1883 – 1963

U95/1/5
File of correspondence; Court Proceedings; wages card of Edward Pilkington and letter from the Divisional Inspector of Mines re Glenboig mine's roof supports. All re Mr Pilkington's case against the Glenboig Union Fireclay Co. Arising from his being injured while removing stoops of clay at Glenboig Mine, 1954. [CLOSED]

      INC.: (2) & (9), The Glenboig Accident Books, detailing dozens of (mostly minor) incidents from 1951 - 1954. Also gives the address and place of work of injured parties.  1951 - 1954         

U95/1/4
Glenboig Union Fireclay Co. Ltd. Journal detailing costs, etc. for the: Glenboig; Cumbernauld; Gartcosh; Castlecary; Dykehead; Bonnymuir; Levenseat 1; Levenseat 2; and Montgreenan Works   1956 - 1963         

U95/1/3
Glenboig Union Fireclay Co. Ltd. Book of production figures and costs for Glenboig, Cumbernauld and Gartcosh Works.   1910 - 1916         

U95/1/2
Glenboig Union Fireclay Co. Ltd. Share Certificate Ledger No. 3. Includes detached index.  1914 - 1936               

U95/1/1/2
Glenboig Union Fireclay Co. Ltd. Register of Share Transfers, 1914 - 1936.             

U95/1/1/1
Glenboig Union Fireclay Co. Ltd. Register of Transfers No. 1 (1883 - 1936). Also includes "Summary of Capital and Shares of the Glenboig Union Fireclay Co. Ltd (1883 - 1913). Numerous trade and newspaper addresses are listed at the front of the book.  1883 - 1936          3/17/2/11

Are NI Electoral registers open and available post 1922 for South Down.  If so what source or location?