The CAA do check logbooks and are fully aware that double logging goes on in the US. If you claim hours when you were not operating as PIC then you could be prosecuted! Log book fraud runs at around £400 a line if convicted and then you could be deemed to be an unsuitable person to hold a licence!
So put it simply, log the hours that you flew as PIC and the other pilot logs the hours he flew as PIC. You are trusted to do this without any form of certification. If however you abuse the situation, you are cheating yourself and any future passengers you carry!