Thanks for all your help with this, everybody! We know know which way to go and what to do.
Do you have a written reply from the contractor stating what his intentions were with respect to your written complaints? I don't think your video opening up some accessories would carry much legal standing as anyone could open up a socket first, undo some screws then close it back up again before doing their own home video. I think the standard principal is that a formal complaint would be submitted direct to the contractor. The contractor should have a reasonable time to address that complaint. If they fail to address your issues you then take it to any trade associations that contractor belongs to and if also applicable trading standards. They would then appoint and independent third party to asses the validity of any complaint. All significant communications need to be in writing or on a recorded telephone calls (I think you have to advise the other party they are being recorded). But as has been pointed out by bringing in your own other electricians you may have left the ground open for the original contractor to deny some responsibility. Your formal contract should be a valid document for trading standards to work with, (I assume both parties are clearly identified on the document and it is signed appropriately), sales of goods act and supply of good and services act. If it is actually dangerous there may be some health and safety issues as well. What do you plan on doing as your next step? Have you paid all the money to the contractor?
The contractor promised, several times, also in writing, to make good the defects. He hasn't done so, and a whole year has passed.
I agree that the videos and photos as such might not be enough. But they will certainly carry a lot of weight. That inspection was not just done by an electrician "from next door", but by two electricians at once, with witnesses present. We also have enough proof for other problems with the electrics, and some of them are still there to see and to inspect. We have the test report (from the original electrician) with test results which cannot be from our installation, not only because they show a whole circuit that simply isn't there. The installation does not comply with the detailed specification we had, and therefore some parts of it don't work and could never have worked. That is evident even from the test report! There is the fact that the electrician who signed the test report is not the one who signed the Part P certificate. The person who signed the Part P certificate never worked on our installation (most probably never even carried out a test!). The evidence is pressing, and the videos and photos are only a small part of it. But whoever sees the rest of the evidence will have no doubt that those videos and pictures are real.
And yes, there were indeed some health and safety issues. We have taken care of them, though, and did not leave the installation in a dangerous state. We don't know yet what is hidden in the walls, but we will find out soon.
The contractor's invoices have all been paid, apart from the last ones. We stopped payment when the first (major) defects appeared and the contractor refused to address them. That amount, though, is nothing compared to the defects that we find everywhere in the building - basically, half the building needs to be rebuilt! (That, too, is all documented, and those items were all valued and priced.)
Anyway, we know which way to go now. ELECSA will be notified. Building Control will carry out an inspection tomorrow as well, we will - for the time being - have to bear the costs of all that, but we now know how to make sure that the contractor will have to pay for the losses we incurred because of all this.