Any safety item must be in writing, there can be a phone call as well, but be it email, SMS, letter, fax it must under HSE rules be in writing, so a fault noted should be on the EICR unless corrected while on site, so you can have a C2 for some thing which is not required under the land lord new laws, which clearly say the DNO equipment is not part of the inspection, and it also says appliances which are not portable should be included where the IET forms would include visual damage to the DNO equipment and would not include items which would be tested when doing the inspection and testing of in service electrical equipment.
The client is free to ask what he wants doing, for example the LABC may as one to do an EICR as if it were an installation certificate before issuing the completion certificate following the current regulations and listing any breaches of current regulations. But that would not be the normal way to do an EICR. This is what makes the land lord law silly, there is no hard and fixed rules as to what is included, including with town houses where there is no loft access except for one house.
There is nothing to say when a C2 has to be given, C1 yes, and you must list faults, but one can simply miss out C2 either C2 or C3 and there is nothing wrong doing that. In fact there is nothing to say you must code items, I have a report for this house done before I moved is which included the electrics so technically is an EICR but better known as home buyers report which was done by a professional which has no coding. It was flawed, but that is beside the point, it is a professional report which includes the state of the electrics, so by definition is an EICR.