It is general practice for electricians to produce the electrical installation certificate, but oddly no law saying he must. If the electrician displays any logo sign writing etc, to show he is a scheme member, then law requires he arranges for a completion certificate to be issued.
However if he has not displayed scheme membership, then up to the owner to apply to the LABC before the work starts, seems to me wrong that the owner is responsible, and often the electrician will do it for the owner, but it is down to the owner to apply to LABC, not the electrician.
I made a mistake, and told the LABC I was taking over the work, as I had thought the builder had done it for my parents, had I known the builder had not notified the work, I would have kept my mouth shut, but you can't un-tell them.
When I misplaced the paperwork, I was told by solicitors they could take out an insurance instead. However since then many councils are publishing the completion and compliance certificates on line, when I tried to get replacements was told it would take 4 months, and would cost how ever long it took the council worker to find them. In other words go away, we do not want to find them.
Here in Powis I can find the certificates on line, Flintshire there are huge gaps, where I know certificate issued, but not showing up on line.
As
@securespark says, an EICR (electrical installation condition report) is nearly the same, and Flintshire would use the EICR to issue the completion certificate if done by an electrician on their list of trusted electricians. It did not matter what qualification or organisations they belonged to, it had to be one on their list.
There is nothing to stop me raising an EICR for my house, even if I had no electrical qualifications, so the LABC would have no idea as to how good, they did accept one from me, as I had letters behind my name, they would not accept one from my son, who had also passed the C&G 2391 exam, which is the inspection and testing qualification, as he did not have anything to show he was trained with his signature. Even when my degree did not teach me inspection and testing.
I would not expect any home to get a clean EICR, there is always some thing, be it old type AC rather than type A RCD's, lack of SPD, which could only be code C3, or some real danger, and we have seen on these pages when home buyers have had EICR done which was clearly an attempt at lowering the price.
If the electrician was a scheme member, then best option is to ask his scheme provider, if not ask solicitor about insurance, personally I would claim I had lost the paperwork, rather than admit I never got it.