The only authoritative source for what you have to log is the UK ANO Article 79. Even under EASA, it will remain the prerogative of each individual authority as to what will be recorded. Beyond that, its a personal flying log book so the holder may log whatever they like.
Normally, an examiner will log as PIC those flights on which he is entitled to act as PIC. If he is acting as an Examiner that requires him to hold an instructor qualification, then if he wants to log it, there is nothing that says he must or can't. Normally, such events would be limited to licensing tests and not operator proficiency checks, that have no licensing function. I don't have an instructor column in my log book! If you are not an instructor what would be the point of logging instructional time, any more than picking flowers?