Presumably because the "law is the law" is and not BS7671 (which is the only 'official' place I know that there is an explicit definition of "consumer unit").
Very true, we have seen with electrical installation where we as electricians have seen it as being fixed wiring up to the equipment, and the equipment as being an other group, although the BS 7671 does not say that, any item for such purposes as generation, conversion, transmission, distribution or utilisation of electrical energy, we see as being equipment not part of the installation.
As to Part P yes it is what requires notification that we often refer to as being Part P. To my mind it does not really matter if the work satisfies the law, what matters is that it is safe.
I don’t want the expense of getting this tested and certified
This is the worrying bit, the idea of doing the work without testing once complete is where I see the problem. The testing of the ELCB/RCD is the main problem, from the point where we first started to use earth rods, we have needed to test, and when the RCD came out I found that cables putting a strain on the terminals can cause them to malfunction, so we need the tester, we can't measure 40 ms with a stop watch. We also need to ensure the earth is good enough, be it the earth rod tester with the test probes, or a loop impedance tester, it needs testing and the equipment to test is expensive both to buy and hire, the latter is expensive due to the cost of calibration after each hire.
As an electrician most of my working life, the test gear was the firms, I did for a short time have my own, but today all I have is the low ohm meter, insulation tester, and multi-meter. I can likely borrow the loop impedance and RCD tester from where I work, but I don't any longer have my own.
The bit which I can't understand is, why would an electricians ask the question to start with?