As said to comply with BS7671 the circuit has three distinct processes.
It is designed, and the person doing the designing has to sign to say it complies.
It is installed, and again the installer has to sign to say it complied.
And it is inspected and tested, and again some one signs to say it has been done.
The form allows for three signatures so the same person does not have to do all three, but the inspection has to be done while it is installed, so the person doing it will stipulate how much is done between visits, so will need to see the trench before the cable goes in, and after it goes in, but before it is back filled, so he can see the sand, and the tiles or tape above and below the cable or ducting.
So to issue a certificate will required the cable to be exposed, of course there has to be a little give and take, so if before laying a tarmac drive a ducting is installed under the drive, the inspector only wants to see either end in most cases. The LABC often do not strictly follow BS7671 they could for example allow you to fit German sockets, which are not allowed by BS7671 but they don't issue an installation certificate, you can get a completion certificate, but only the person/s doing the work can issue an installation certificate. Often the LABC will issue a completion certificate on the strength of an EICR and there is no legal requirement for an installation certificate and it depends on where you live if the work needs registering.
So you may not "NEED" the paperwork, but if you do then you will have to make it out, blank forms are on the IET web site, but looking at around £300 for a tester.