As its a 1910 Bayonet, so pre war plus if its Durham school as Peter points out then I doubt its a battalion. Would say any school or cadet forces were relieved of there equipment at the start of WW1 so I,m guessing this was the change in marking,
Regarding the DM I,m only going by notes I received many years ago......... very similar to ones below in the 2 links.
http://www.martinihenry.com/units.htm
http://oldmilitarymarkings.com/brit_bayo.html