@CloverRiver I have caught up again with your latest posts with new details, particularly your joint mortgage.
I doubt you have any chance of arguing that you are not cohabiting in light of this. Also, if his share of the equity/any rental income is or will be more than £16kish, does that not preclude him from UC. If he has to force a sale of your joint home in order to afford a new place, how does that help you? Can you afford to buy him out?
If not, another (and possibly happier all round solution) would be to loan your DP the money (with agreed interest etc) he needs for the fees, with his equity in your joint home put up as surety against default. This would protect you financially, allow you all to remain living together and for the boy to stay in his school. If DP won't agree to this, then you can validly question whether he is trying to take advantage of you and act accordingly.