BS 7671 requires inspection and testing after each job, there are two forms, the electrical installation certificate and the minor works certificate, but BS 7671 is not law, but can be used in a court of law.
It depends where you live, England and Wales are not the same, in England if it did not involve a new circuit then just minor works certificate. If new circuit then installation certificate and also needs notifying, in Wales all work in kitchen needs notifying.
There are two methods, one is through the LABC and you will get a completion certificate, the other uses a scheme provider and you get a compliance certificate.
It matter how the electrician advertises himself, if he no where be it side of van or paper work, or website says he is a scheme member then it is up to the owner to inform LABC, if however he shows he is a scheme member anywhere then the electrician needs to sort it out out, in England many electricians feel the fees are silly to be able to fit consumer units, new circuits or work in bathrooms, so no longer bother keeping up their membership, but have not got around to removing the logos.
So in Wales he has no option he must issue the paperwork, as even if you deal with the LABC you need the paper work i.e. minor works from him to submit to the LABC, it cost last time a did it £100 plus vat for first £2000 worth of work. Yes bit silly as most electrical jobs no where near the £2000 limit, in England the council can set it's own rates, but must define "New Circuit".
Circuit is easy = An assembly of electrical equipment supplied from the same origin and protected against overcurrent by the same protective device(s).
It is the "New" which is hard, so if a MCB feed a shower and is no longer used for that, if re-wired to an oven, it could be said not new, in fact even if only the MCB existed then one could claim not new, it is for the courts to decide, and it is unlikely to go to court, as if the LABC say that's new pay up or we go to court, people will just pay up.
The problem with LABC you can't untell them. I had this, builder ran off, I thought all above board, so went to LABC and said I am taking over the job, turns out he did not tell them, and it is the owner who must ensure it is done, although most builders do it for the owner.
As an electrician I would always issue a certificate, it protects me, if it says the ELI is 1.23Ω and after an accident it is measured at 5Ω I can say to HSE it did not measure that when I tested some one must have been messing with it. However if I don't issue a certificate specially if some thing which needs registering with LABC the fact I have not issued a certificate points the finger at me. I can say I thought the owner was doing the registering if issued, rather clear that was not the case if I don't issue one.
OK I can fudge up results and not test, but am likely to get caught out, so not worth the risk. Filling in minor works or installation certificate acts as a check list, there are times I can see why an electrician would not want to raise paperwork, for example when he has added to a circuit not RCD protected, he knows jolly well he needs to do something which he has omitted. House with old Wylex fusebox and small job which would cost £50 say add a new socket, jumps to £300 or more as need to change fusebox for a consumer unit. However he should tell you that a new consumer unit is required, and when he realises to person just does not have the money I can understand him saying OK I will fit socket cash in hand no paperwork.
When I hear paperwork not issued I think why, what rules has he broken so he does not want his name on the job?