ANO Article 140 prohibits "aerial work" in foreign reg planes, unless you have the permission of the Secy of State (actually the Dept for Transport).
So... what kinds of things will they give permission for?
Certainly the owner(s) receiving training in the plane - I've had that one a few times, enabling me to pay the instructor. (If the instructor did not charge me for the flight, no permission is required). Last time I looked at the DfT website, they gave detailed guidelines on what classes of owners they will give the permission to (e.g. max 4 owners, etc).
The rest is a grey area which they don't advertise. However loads of commercial ops very visibly take place using foreign reg planes, and whole airlines operate with foreign reg planes. This is outside my area of experience but I believe that if you have an AOC then you can do "anything" - the CAA is keen to get the AOC fee, and an AOC ensures that you are not operating with a lower cost base than a G-reg operator doing the same work. "AOC busting" is always vigorously enforced by the CAA anyway. I also vaguely recall reading some stuff on the DfT website that UK G-reg operators have the right to object to another UK operator doing the same thing with say an N-reg.
However, there is one thing you can do with a CPL/IR, with no permission being required: be a paid pilot for the plane's owner (individual or a business). No AOC is required for this, and this is the basis of corporate / executive jet ops worldwide.