The cap badge is the Middlesex Regiment [full title Duke of Cambridge's Own (Middlesex Regiment)] and the lack of a Medal (roll) Index Card would appear to confirm the story that he never went overseas.
You should still check on Ancestry for a service file for him, if nothing is found there is nowhere else to look.
If he remained in the UK he would have served in one of the Middlesex's Reserve battalion's (see
http://www.1914-1918.net/msex.htm )but identifying which one will be very difficult without a service number or his records. Your only hope would be if there is a surviving 1918 Absent Voters List for where he lived.