Many clubs require an instructors rating for passenger carrying for (amongst other reasons) one of insurance.
If the P1 is a BGA rated instructor then they will be fully insured and it's all 'sorted'.
If however the P1 does not have such a rating then in the event of an accident the P1 may well be personally liable for any claims against them by the passenger or indeed from third parties on the ground as the club may not have insurance to cover this.
It also makes it a lot easier if P1 is an instructor as they can then let the passenger handle the aircraft's controls wheras I think non instructor pilots holding a club issued passenger carrying rating may not be allowed to permit this - partly because if they do then it becomes de-facto instruction by the P1.