Sebatian, until the late 1980's the Home Office produced a document/handbook entitled "Police War Duties Manual". What they envisaged was that in the break down of society following an attack, by bombing or invasion, Police Forces would form their officers into mobile columns which would be able to deploy wherever they were needed. In latter years the policy dictated that these columns would be made up of three transport vehicles, with command. The strength of these mobile columns would be at least 30 constables, 2 sergeants and 1 Inspector.
They were supposed to be fairly self sufficient, although no doubt it was thought that in dire circumstances columns would merge to form larger units. This policy was replaced by the PSU:- Police Support Unit, concept in later years. The theory was that concentrated resources would better to deploy rather than one or two officers here and there. As far as I know there is also room within the policy to have the officers armed, at least a percentage of them would be. The policies relating to armed Police during the period you mention were far more "flexible" than is currently the policy.
In fact until the late 1960's, in London at least, firearms training was very haphazard, and often firearms would just be issued to any officers who had military experience for example. Certainly in the event of war, Emergency Powers legislation would be enacted, which would entail a more draconian style of law enforcement than that prevailing in peacetime.
Hope this is of some help. I think I still have my copy of that manual somewhere, I must dig it out and check some of the bizarre rules etc.