Receiving instruction in your own aircraft NOT for the issue of a licence or rating is absolutely not aerial work
Correct, but paying the instructor is.
That's why, with an N-reg, you need the DfT permission if you pay him. Unless you do the training outside UK airspace, etc, etc.
It is interesting to note that the ANO was so recently amended to rank e.g. a F- or D-reg the same as a G-reg. It was my view for years that such an exclusion was illegal, but the CAA is going to lose a lot of revenue if schools use non-G-reg EU fleets. Perhaps they won't approve the school?