These all seem to be reasonable solutions, if a little stop-gappy.  I think my problem is that I am seeing this as an outsider to this UK group and the UK group might be seeing the article as a group of insiders writing for insiders.  My initial problem with the article was that it is unclear and allows different incompatible readings.  "Administrative geography" certainly makes the article more consistent, but I'm not sure it makes the title more understandable (unless, of course, you are a geographer or know all the branches of geography).  To benefit neophytes (perhaps I presume too much in thinking this is the intended audience of wikipedia and any other encyclopedia articles) on the subject which this article addresses, I would make the following suggestions.  1) Gut as much of the introduction as possible regarding the four countries and, instead, refer people to that article (since it already exists; which would also resolve some problems people have with repetition between these two articles.  2) Explain what "administrative geography" addresses (e.g., national and local government hierarchies) and how this relates to this article.  3) For the love of God, rename (to whatever is appropriate) the section entitled "In the UK" (or eliminate this title) because it serves no purpose whatsoeverperhaps to "contemporary administration" or something that transitions from "History"; although for reasons beyond my comprehension, some people are apparently wedded till death to that vacuous phrase (i.e., In the UK).  4) Move the last paragraph of the Intro (beginning with "Historically...") to the History section or exapnd on the themes it introduces. 5) Identify the referent of "This structure" in the History section (i.e., answer the question, "What structure?").  6) Follow strict style guidelines for the terms "division[s]" and "subdivision[s]" throughout this article if either is a significant concept for this article.  7) Incorporate the "Parliamentary representation" section into the section preceding it.  This would give a structure of [Introduction], History, Contemporary Administration (or whatever), Informal (Sub)Divisions, International (Sub)Divisions. As things stand, having a separate section for informal divisions suggests the rest of the article is about formal divisions, which would be fine if the sections reflected a more transparent and sensible organization to the article currently lacking.