P/UT time in Canada would not
Nice and easy here in Canada. There is no such thing as P/UT when building towards the CPL (or any other license or rating below the ATPL). It's either PIC or Dual.
PICUS (the same basic thing as P/UT) is available for the ATPL. It is only available when the air operator (
not a flight school) you are working for is approved to do so in its training manual, and then only with the approval of the Captain (who sometimes has a company form to complete). There are other requirements too, but I can't recall them all off the top of my head. What I do remember is that many air operators I worked for had a minimum time with the company before they permitted you to apply for PICUS (my previous company had a first recurrent restriction, so 6 months) In the pilot's logbook, PICUS was logged in one of the blank columns, not in the PIC column.
If I then go to Canada and fly a C reg plane, do another 15nm from the aerodrome, do some air exercises, then fly back, I log this as PIC 1hr and again in the UK cross country column list 1hr and in the Canada cross country column list 0hr. Is that the right way of doing it?
You could log it like that, or you could log the hours based on the most restrictive country - that's what I did when I did the same thing as you, but between Canada and New Zealand. in your case, you'd only log cross-country time on either a G- or C-registered airplane when you went to another airport. Outside of regulatory requirements though, consider the purpose of cross-country training, be it dual or solo. It's not simply heading out to the practice area which is in full view of the airport you left and staying in your comfort zone. It's meant to get you used to going somewhere you're not familiar with while being able to continue to navigate to another airport all while interacting with the airspace and aircraft around you. I'm somewhat surprised you can log cross-country without going to another airport, but that's the beauty of different regulations!