I think we're all agreeing. My understanding is:
In the UK, flying a G-reg aircraft that only requires one crewmember, only one person can log flight time at any one time. If two of you share a trip, you can share the total time - for example, start time 0900, end time 1200, log 90 minutes each.
If one of the two has an FAA IR and is flying a G-reg under the hood to keep FAA IR currency, and the other is lookout (within the terms of his licence and ratings), then only the "P1" can log it.
If it's N-reg, whether in the UK or the USA, both the "P1" and the "Safety pilot" can log it as P1. Different rules.
Hope that's right!