Sprawler,
This is indeed a tricky point and does need to be addressed by the CAA. With an instructor onboard, it depends on how you read the regulations.
Argument #1.
The instructor is there to provide instruction to ensure that you can satisfy the club checkout requirements. Hence, you are Pu/t and the FI is P1.
Argument #2.
Legally you are capable of operating that aircraft with or without the instructor present. An instructional flight requires two pilots. One instructor and yourself as the other pilot. Hence you could argue that the instructor is commander and you are captain of this flight. Assuming that the instructor does not have to interfer with the conduct of your flight, you could be said to be PICUS (note: slight difference to P1/s). You are exercising the priviledges of your licence under supervision of the commander.
Personally, unless you really need the P1 time, I would err on the side of caution and log it as Pu/t.