I have heard people refer to themselves as partP qualified / PartP electrician...
Doesn't make it right, and you have to wonder what else they c.b.a. to get right.
Then how would you describe the process of notifying electrical work for the purpose of compliance with part P?
I wouldn't because there isn't, and never has been, any such requirement - Part P is easy enough to read, it's only one paragraph and basically says "installations must be safe". Thete is no mention of notification or scam membership.
The confusion is that "Part P" came in at the same time as the notification requirements in the 2010 building regs - so many people who really should know better were confused, and quite a few charlatans deliberately muddied the waters for their own gain.
So answering the question I think you meant to ask, I would just refer to "notification", or "building regs notification".
As a thought, how many other trades refer to "Part X" (substitute appropriate section for X) registeted ? Can't think of any ? Windows have the same requirement, either use a scheme member or notify LABC, but you don't see them advertising or talking about Part X. They advertise membership of (e.g.) FENSA in the same way a lecky advertises NICEIC or Napit.
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It used to be part P but that was done away with ...
As above, it was NEVER Part P - other than in confused minds.