Malcolm, if you fit one of these small badges on a glengarry it looks absolutely lost. But the BW seem to produce a regular supply of these half or 1/3 rd size patterns from 1881-1936 see various examples from my collection. I can see that the OSD patterns with blades would suit the adjutants cap. It has been suggested that they were worn on the glengarry only in mess dress? The problem is I have never seen any photographic evidence showing these badges in use! But in the absence of further information I would term them a small glengarry badge.
Ron.