I thought Channel Islands instructors regularly took their students into France while training. Doesn't that rather imply a UK FI in a G-reg aircraft can do that?
My FI (back in the dark ages) did some training with me, pre-PPL, to France and back, and he thought it was legal. The CAA inspected my logbook when they were issuing my PPL (even ticked bits of it) and didn't object either.