I knew, Fred - the instant I mentioned courts and judges - that YOU would appear! All I can tell you is that the answer I gave is one I got from somewhere many years ago and have always just 'believed'. In my support, within the opening paragraph of the OED's entry on 'Home Counties, it says, "Home Circuit. The assize circuit which has London as its centre." (As regards your When? query, this statement is a quote from a document dated 1898.)
Under 'circuit' in the legal sense, to which the OED cross-refers, it lists: "Northern, North Eastern, Midland, Western, Oxford, HOME or South Eastern, North Wales, South Wales." It would seem, therefore, that the OED believes 'Home' is an alternative name for 'South Eastern', as you call it.
Given that the OED clearly ties Home Counties and Home Circuit together, as well as listing a Home Circuit, it seemed quite reasonable for me to do so as well. If wrong, I'm happy to stand corrected, so perhaps you need to do a Victoria Coren 'Balderdash and Piffle' and approach the editors of the OED, too. Cheers