HewG,

Two other possible explainations for a couple of the police nicknames you quote:
'Plod' - Possibly from Mr. Plod the Policeman, a chatacter in the 'Noddy' books of Enid Blyton who displays the 'plodding' characteristics of the local country policeman in all of her 'whodunnits'and just waiting to be dazzled by the brilliance of her detective character).

Old Bill - This may well derive from assoiciation with the Old Bailey, however, after the Great War, the popular cartoonist, Bruce Bairnefather was commissioned to produce a series of recruiting posters for (I believe) the Metropolitan Police, these involved his two most famous characters 'Ole Bill' and 'Alf'. In addition, between the wars, a great many policemen were ex-soldiers and, I am informed, many retained the moustaches which were compulsary in the British Army until 1916, giving them the appearance of the Bairnesfather character