Proxus,
The FARs are different to the JARs in this respect. Under FARs, two pilots can both log time on a single-pilot aircraft under certain circumstances, e.g. if one is safety pilot. Can't remember the exact rules. But under JAR, no - the only way two pilots can both log time on a single-pilot aircraft under JARs is if one is an instructor/examiner.
GID44, as linked to above, is an excellent reference for the UK (JAR) rules. The only thing which it fails to cover, and which is discussed repeatedly in Private Flying, is how to log non-instructional time with an instructor (e.g. if you go out of whatever your club's currency rules are, or just fancy an hour to boost your confidence, etc.)
FFF
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Edit, because, having re-read your post, Proxus, it sounds like the P1 in your example is a student pilot? In this case, it is illegal for him to carry a passenger at all, let alone for the passenger to log the time.