OK, now I admit that I've screwed up. In fact, I have scrawled on the bottom of that AIC a whole bunch of notes from a seminar which was discussing the ambiguity of the AIC. My notes say "record as P1/us".
Bad excuse, I know but, I even queried this at my last Instructor Reval.
The point is that P1/us is - in my mind - a more legal way of recording such flying since P/ut would be dodgy to log on aircraft not on public cat C of A's but not wholly owned by the pilot (e.g. group a/c) or indeed on foreign registered aircraft.
I can't see a problem with P1/us when used in this way; it delineates Training As Part Of A Recognised Course from just flying with an instructor.
If you read AIC127/1999 para. 2.3.1 (the section to which the irrascible Booky refers) it is terribly ambigous as to whether the logbook is signed (no need to sign P/ut normally remember!) and the 'STUDENT' records instruction or whether the 'INSTRUCTOR' then records that flight as Instruction Given so that it count towards the thre-yearly instructor totals!
Have fun