It's obviously legal in UK airspace...
Any country could ban it within its own airspace, but EASA regs (are there any covering this?) might over-ride that.
N-reg is complicated. Illegal in UK airspace under ANO Art 225 and in any case complicated due to the FAA
"common purpose test".
I have a letter from the head of French Customs which confirms they will not apply Cabotage to private flights, which is very kind of them
but obviously if they want to go for you for cabotage then they have already decided it wasn't a private flight
This was obtained by somebody, a few years ago, regarding cost shared flights
within France.