You may well be right about his record not surviving, it certainly doesn't seem to appear.
The one for whom you find the medal card also has no service record. All one can glean from that is that man served overseas with 1/8th Battalion Middlesex. Similar numbers suggest he entered service in early 1917.
A possible scenario is that your man didn't serve overseas. Although the rules did get bent, he was only just 18 when the war ended, under the official age of 19 for overseas. Thus he would have no medal card either. The Middlesex had UK based two Graduated Battalions (for young soldiers) and one Young Soldiers Battalion (recruits).
MaxD
MaxD