PICUS
Sciolistes - I urge you to speak with the FCL division at the CAA - believe me, I went through this mill. They do not accept hours recorded as PICUS to be PIC unless with a CAA examiner doing a LPC, Skills test or rating renewal - and you PASS in full, not partial.
A school rep. doing a local (ie for their purposes) checkflight is to be logged as P/UT.
PICUS/P1.S conditions are listed in the table in LASORS (2008), section A, Appendix B, cases B and J; J is the one that applies to single pilot operation. Do NOT listen to the school - they are unwittingly (?) wrong and it will ultimately come and bite YOUR wallet when the final reckoning happens. I had to recover 15 hours. (c. £3000)
As an aside, 'safety pilots' are viewed with great suspicion by the UK CAA. The chances are that, despite your taking what you might think is the prudent approach to initial exposure to foreign airspace, they will assume your safety pilot to be PIC. I fell foul of local regulations not allowing foreign language speakers and solo flight in US airspace before the issue of a temporary airman's certificate.
Patrick.