It's obviously true that a DfT permission is needed only if the "aerial work" is done in UK airspace, but I cannot see why an instructor cannot be just a passenger on a preceeding flight - provided obviously that the LHS already has the required papers for that flight.
If an instructor could not be a passenger on a mutually agreed flight then any instructor could potentially never be a passenger and many flights would be instantly illegal for all sorts of reasons.
I hate to over-use the word "obviously" (one sees it on TV all the time, usually from less than bright people
) but obviously it depends on what exactly the instructor is charging you for. If he bills you a daily rate then calling himself "passenger" on a flight that day is going to be pushing it a bit
But if he bills you hourly, and only for the hours takeoff-landing in French airspace, how can there be a problem?
Loads of UK schools do fly-outs where a group of planes fly somewhere, and there are several instructors "aboard" and predictably the whole thing is rigged so as to maximise revenue by putting an instructor in the RHS when there is a "student" in the LHS. That way the school gets the self fly hire rate plus the instruction rate, on every leg. But there is no presumption of instruction if there is an instructor in the RHS and the LHS already has a PPL, or whatever.
In the end you have to go along with the wishes of whoever you are working with, however.