Nuclear weapon
What license ave you just applied for? Shiny blue - in my day PPL covers were dog efflux
brown
If you had not received a PPL, then IMHO you would log the time as P/ut, with the FI as P1.
If you were PPL qualified, then a cross channel trip is neither a formal test nor a lesson from the CAA syllabus, so logic suggests that you would be P1, unless a specific training activity was briefed, agreed and executed.
Otherwise, I would suggest that any intructor input was from a highly qualified passenger, unless he took over the controls.