::We presently have 3 references in the introduction that each state Britain and Ireland - "is becoming [the] preferred official usage...", "Nowadays" it is the "most favoured expression..." and that the term "British Isles" - "should best be avoided". The last quoted reference according to the Guardian newspaper. So it's not your mere "one source"  as claimed. Despite these 3 references however, bizarrely, none of these well referenced facts are to be seen in the introduction of this article. Canterbury Tail's, you ask - "Why should it be in the lead...?" - because it is now the most favoured and preferred official alternative term. 
Lastly, on a practical standpoint, say for example you were looking for a new book on the types of birds/wildlife in general for the region, you'd be hard pressed to find any such modern books with "British Isles" in the title. Why? Because "Britain and Ireland" has become the "preferred official usage". See ->
Crossley ID Guide: Britain and Ireland (The Crossley ID Guides) (published 2013) 
Bird Atlas 2007-11: The Breeding and Wintering Birds of Britain and Ireland (British Trust for Ornithology) etc.
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