Be aware, the Kew Records office holds very few WW1 war diaries, most were retained by the Regiments (fortunately) the archived ones from WW1 were mostly destroyed in the WW2 Blitz. Kew Records are still trying to sort out a lot of the partially burnt paperwork. Try the Regiment's museum.
I had a similar case with my Father (RFA), he was given a Mention in Despatches at Mons, 1914 and the MM in 1916, yet I could find no mention of the MM apart from the medal cards held at Kew. I did find out that a lot of MM's, earlier than March 1916 (when the MM was first announced) were back dated ones given to some M.I.D recipients later in the war. This may account for the 1918 issue dated 1915. If this was the case then the M.I.D was withdrawn and wouldn't show on the Kew medals cards.
I eventually (luckily last year) found the war diaries at the Royal Artillay museum in Woolwich London. They were on loan to the Museum and had details of the engagements for my Father's M.I.D and MM. As has been said, citations for the MM were given to the receiver but not recorded outside of the diaries.
I was fortunate to find my Father's battery Commander's, Brigade Commander's and the Regimental diaries for the 1914 to 1917 period and all three had full details of him in them. Good luck with the search.
Col
