Before we move onto "New", as I said before you are choosing to quote the BS7671 definition of "a circuit", but I don't know why you think thi was what was in the mind of those who wrote the legislation requiring notification (in England) of the installation of a 'new circuit'.So question is New.
The BS7671 definition itself has not, at least in my opinion, been properly through. Even forgetting the issue of FCUs (the failure to 'exempt' which I personally believe was probably an oversight), it really ought to define a "circuit" as being those things protected by the same most downstream OPD - since, as literally written, it could be taken to mean not only that everything in an installation was "one circuit" (protected by the cutout fuse but even that everything i every installation on the same phase in a street was also just "one circuit" (protected by the OPD at the substation/transformer.
As for 'New', as I implied, I think that virtually everyone (probably including the hypothetical Courts which you so much love to talk about!) has a fairly clear common-sense view of what the word means, along the general lines of "the appearance of something which was not previously present".
"Part P" is actually "Part P of The Building Regulations 2010", which is a Statutory Instrument produced by the Secretary of State under powers bestowed on him/her by The Building Act 1984 - hence very much "a law".As as to Part P, is it a law or a regulation?
However, as we know, that "Part P" is simply one sentence, which says that electrical work has to be undertaken 'safely'. Nothing more - and certainly nothing 'specific'.
Kind Regards, John