First up, NO, you don`t need someone from the NIC. You
need someone who is Part P registered & can self-certificate their own work. They could be from the NIC, or equally from Elecsa, or from Napit. Despite what your Building Control have misinformed you, none are preferable over another in this scenario. Period.
If you are to have notifiable work done (as you are proposing) by someone who cannot self-certificate - whether it be a non Part P spark or just as equally by yourself - then you will need to inform BC in advance & pay whatever charges they feel like slapping on for Inspection & Testing afterward (by a 3rd party) Be warned here, incredibly, this can be as much as £300! Kinda expensive for a few extra sockets & lights eh!
Gotta admit, i`m puzzled at your mention of "accreditation for a part P course" as a pre-requesite for your chosen electrician. They surely said "registered with a Part P body" or similiar? (Please be kind enough to clarify) If not, then they themselves are breaking their own Part P of the Building Regulations - which wouldn`t surprise too many of us here, i`m sure.
If, for whatever reason he fails to get assessed, or they take exception to the fact he didn`t notify BC in advance, then
you would have been put in a precarious position. Only the person erecting the work can sign it off with an Electrical Installation Certificate so the lovely Building Control would have to be approached to aquire a `Regularisation Certificate`

Not a great position to be in.
You have been fairly warned of the possible pitfalls.
But the choice is yours
