The London Gazette has references to members of what is probably this family's business, but also to EH Shrager who served in 23rd Battalion, Middlesex Regiment as you know.
He was an officer, so would not have a regimental or other number.
He was awarded the Military Cross for gallantry, and a citation was published.
If you go to the London Gazette website:
http://www.london-gazette.co.ukand enter Shrager in the 'exact' box, and put date of 1 Jan 1914 to 31 Dec 1919 you will find these references, including the citation which appeared in issue 31480, supplement dated 30 July 1919, pp.9773.
There should be two medal index cards for him, one for the MC, the other for campaign medals. The second should be available via Ancestry, free this week.
Officers' papers are not among those on Ancestry - someone can possibly advise you how to find them.
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