If a consumer unit is damaged and needs replacing before power is restored it would be reasonable to change then test. As a result there is nothing saying testing should be done before starting the work.
So although to avoid and arguments most electricians will test before they start there is nothing to say they must.
The C&G 2391 or 2392 is not required before some one can test. Neither is C&G2382 (17th Edition) all that is required is that he has the knowledge this could be gained without taking any formal qualifications.
Building control will in the fullness of time be notified but as to whom does this will depend on circumstances for example where a builder is adding an extension this could be all done by the builder or when many trades are involved could be down to clerk of works who may be the house owner who would have no idea as to what has been done he may be just forwarding on paperwork.
There are exceptions to most rules and for example fitting a disabled kitchen, or wet room where there are no LABC charges electricians may go down the direct option, rather than through the scheme operator, so although we can state the normal this does not mean it's the only way.
The LABC can set requirements, when I used them, my son was not permitted to sign the installation certificate, the inspector insisted I did the testing. We both held the 2391, but he would not takes my sons signature. He could have tested himself or had an outside firm do the testing. Once the LABC take the fee they are responsible for site safety, and what they says goes however daft it seems.
Although most builders, and electricians will do all the work of informing the LABC it is the responsibility of the owner to ensure it is done. I have seen problems where the electrician thought the builder was doing it and the builder thought the electrician was a scheme member, and that the electrician was doing it, and once the LABC found out it was made very plain it was down to the owner to insure it was done, which did seem a little unfair. However since the LABC at that time did not issue permits to work and it was all word of mouth. Get an electrician who says the owner is doing it all and very little can be done if the work is A1.
I would say not issuing an electrical installation certificate would show the electrician knew he was doing something wrong, but this is issued to guy ordering work, in our case the builder, so since we never managed to get the builder when he ran off into the hills, we could not prove the electrician was trying to pull a fast one.
I was in a way very lucky in that both my son and I are both electricians, and could take over the job and sort it out when the builder did a runner. We found being honest to the LABC worked, and the inspector was helpful however until that point we thought the people doing the work had to inform the LABC, but as I say it was pointed out that was not the case the owner is ultimately responsible.