My interpretation is exactly the same as Evo's - the only time you can log P1US on a single-pilot aircraft is for a successful skills test. However, I emphasise that this is my interpretation - the rules themselves are not entirely clear.
The information used to be in a document called GID44, and if you search these forums for GID44 you'll find lots of discussion. GID44 doesn't exist now, the regulations have been moved to LASORS instead, but the only part of LASORS I can find on-line is LAS, and the regulations you're looking for are in ORS, so unless someone can find the link you'll have to get a hard copy.
But basically, the only time P1US is mentioned for single-pilot aircraft is for a successful skills test. But it doesn't mention the word "only" and so it doesn't explicitly preclude you from logging other time as P1US. And there is nothing anywhere which describes how to log time with an instructor when you are not training for a license or a rating. Therefore, some people choose to interpret this as meaning that you can use P1US for the type of flight you're talking about, and some don't. It's all very confusing, and clarification from the CAA is long overdue.
My reason for saying this time should be logged as P1UT and not P1US is based on being conservative - certainly no one is ever going to tell you that P1UT is wrong, whereas they might tell you that P1US is wrong.
(As Evo says, the other option is for you to log P1, and your instructor doesn't log at all. If this is the case, you are in charge, and your instructor is no more entitled to tell you what to do when you're flying than any other passenger would be - although of course you might choose to use your privileges as P1 to ask him for advice. If you choose to log time in this way, it should be agreed with your instructor before the flight, IMO.)
FFF
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