Part P is the building regulations, but often what we think of being part P is the requirement under that regulations to notify some work. This varies between England and Wales with Scotland having a completely different system which in essence does the same. So do need to know where your living, in Wales where I live I would think this work is notifiable, but not too sure from your description. Part P is law, however the BS7671 which we all tend to call the electrical regulations are not law. BS7671 requires one to raise a minor works or installation certificate with all work done, in the main to fill in the certificate means one has to test plus one should also inspect, this act of inspection and testing can highlight errors. The errors are not only about the new work but also the existing installation. One can connect up all the earth wires correctly, but without testing you have no idea if the earth wire is actually earthed.
It is not only kitchen fitters and other non electrical people who skimp on the testing, council did some work for my mother, and we never got the paperwork, and I know it does not comply, the socket is not RCD protected, as to if they did not provide paperwork because they knew it did not comply, or simply the guy left his meters behind is unclear.
The requirement for RCD protection is a real problem when doing minor works, move a socket 8 inches up or down the wall is not a big job, but to provide RCD protection for a socket which did not originally have RCD protection can be expensive. £12 for RCD socket, instead of £2 for a standard one, plus if cables buried use of special cable which does not require RCD protection.
In the main using a plug in tester like the EZ150 one can avoid most of the problems which full testing would highlight, however it would not give you the readings to put on a minor works certificate. I full test set is expensive, and it needs calibrating on a regular basis which is all well and good when you use it every day. But if you only use it once every couple of weeks then I can see why any workman would not want to either buy or maintain the test gear.
For you it is a case of should or can you do anything about it? The EZ150 does a loop test and costs around £50 to my mine I would be happy plugging one into each socket and if it passes saying good enough without the paperwork. But if you want to sell the house that could be a problem, so you have to decide what to do.
As to the Part P that does nothing, it is just an expensive bit of paper, as to minor works certificate that does show it has been tested and is worth a lot more even if it's not legally required.