Checked with LAA today.It appears that there are some RF5s on permit to fly .
This arose some time back as the support was not available to enable them to carry on with a CofA.(without going into detail that was the criteria then)
however this subsequently changed so they belong to that small batch of aircraft where you can be on a permit or CofA even though it is the same aircraft.
The answer to your original question is slightly complicated but in essance is..No LAA permit aircraft are cleared for reward.So for you to charge for tuition it has to be on a C ofA which can be easa or BGA.
There is however a loop hole that basically allows owners to train in their own permit aircraft provided no reward changes hands.Thats a slight simplification but should answer your question.