There are some marked differences in how different countries equip and deploy/use their MP units and resources (ex-Reservist RMP(v) here), but once the lines of communitcations are stuffed to hell and back, it'll be down to local control and chain of command; British MPs aren't used as facility guards (except of their own facilities), for example, although they do run control/information posts on military routes, run policing patrols in occupied areas,and instruct other units in what to do with their EPOWs. YMMV
WRT other units, signallers, mechanics, admin types, medical facilities, stores units (such as they could given the problem of looking after the stores and ammunition) will likely have been pulled back when the tactical nukes dropped, Royal Air Force Police and RAF Regiment will have been protecting the air bases ("RAF Stations") and detachments (Harriers will have gone to pre-arranged dispersal points off-base, and when their stations got nuked, the OCs will likely have tried to withdraw them to safer places nearer the UK.
Naval forces will not have forward deployed as much (if at all), but given the bases are fixed, will likely have turned into rapidly-expanding clouds of radioactive vapour. Units at sea would have been left with little alternative than to try to find a friendly port after that.
Stations, camps, and bases in the UK will all have been targeted. You can assume they aren't much more than radioactive glass bowls by now. Whitehall and other command and communication posts will likewise be smoking holes in the ground.
Thus, without any meaningful strategic command and control, everyone's using their own initiative, their own preferences and priorities to likely strike out for home, using whatever they can, wherever they can, to get home.
Those that ARE home on their own soil (what's left of it) will likely form quasi-medieval zones of control, and since they have the guns, they'll rule the roost locally.
Welcome to the new dark ages
