As
@JohnW2 says there is nothing which says how much should be tested or any hard an fast rule what is Code C2 and what is code C3, or what is simply outside of the remit and what gets code F1, the EICR is not designed as a legal document.
So back in 2005 when I had dealings with the LABC they did not simply say we want an EICR but said we want one done by some one on our list of approved testers.
We said to prevent any argument we wanted a tester higher qualified than myself, so at least level 5, really needed to be level 6, and there was no one on their list over level 3, which meant in real terms if they found anything they did not like, it would result in a court case to decide who was correct, and there was a possibility I would win, and the LABC backed down as it seemed a pointless exercise, as I had already stated I was unlikely to put parents at risk.
In hind sight it was silly, the LABC inspector should have looked at the completed work, I may have wanted to get rid of my parents, he should have visited at completion and checked on the work.
But the argument is still valid, for an inspector to decide an installation is potentially dangerous he needs to be able to show his expertise is higher than the expertise of the person he is inspecting the work of. If he can show it does not comply with regulations that does not automatically mean it is dangerous.
As the electrical engineer for a concrete works, I had to write the requirements, and I would always include "Must comply with current BS7671 unless prior agreement is made and be at least as safe as any previous system." this allowed me to call them back to change things even if not dangerous should they not comply.
On the one time I tried to use the clause, I was vetoed by the boss, who said we can't afford to upset him, he is the only person we can find with the software and expertise we need. It was over the dumping of 1 cubic meter of concrete on the back of my colleague when the system failed to detect it had over shot the release point. He was not hurt.
The LABC can insist that the installation is better than the regulations and law require, but it has to be their inspector, not a third party one, so in my case the LABC inspector insisted on an extractor fan even when law did not require one, as the window of the wet room if open would allow visitors to see inside the wet room.
But at end of day, if the LABC inspector issues a completion certificate then there is very little you can do unless it really goes drastically wrong, even where the LABC inspector failed to notice the houses were built 3 foot too low so they flooded before the water escaped over the road when culvert became blocked, it resulted in a massive court case, one would have thought it was cut and dried, the LABC inspector had clearly failed in his duty, but it still went to court and blame was proportioned between LABC and builder.
There is a limit to what can be blamed on any one party.