CAP 413 manual very clearly states that it's advisable to includethe airport name, as well as the aircraft type in the call.
It does not state it is advisable to include the airport name, it specifies it will be included.
It does not state that it is advisable to include the aircraft type, it specifies that this may be included if it does not cause confusion. That extra identification may also be generic rather than type, i.e. 'helicopter.'
Of course, the aircraft type will be given on initial call to a ground station.
You still do not seem to understand what these British manuals really mean, but I put that down to your North American culture, since that often applies the other way, too.
Coming from a minor European country, I do not have any great sense of righteousness or 'made here' and just get on with trying to fit in with everyone's local ways of working.
If you feel so strongly, why don't you write to the CAA and tell them where they got it wrong?