Will an EICR actually establish the circuit arrangement - in the sense of establishing the configuration of the wiring? Presumably if it does it will provide a schematic wiring diagram (of, in this case, the connection of each socket, fan etc to the consumer unit)? I have seen a couple of EICR certificates and I am pretty sure than none of them included, or had appended, wiring schematics.This is why an EICR is a must, so that the current circuit arrangements can be established before working out what to do next.
By 'etc.' yes I meant all other relevant tests.