Pianorak
I am no lawyer but looked into this 2yrs ago for probably the same reason as you, in my case doing an IMCR in a group owned Private CofA plane.
One cannot use a Private CofA plane for training for the initial award of any License or a Rating, unless the person getting the training owns the plane outright (or is a 100% owner of a ltd co which owns the plane).
Apparently there is a loophole: the instructor does the flying FOC and charges you £100/hr (or whatever) for "ground school".
There is another problem I recall: an instructor cannot work freelance nowadays, training must be done under an FTO, which might simply mean you have to join the flying school... £50?
Check the insurance, of course.