I used to pay cash, now most don’t accept that either although with my last car which i picked up in june you could pay with a card but only up to a certain amount £1k if i remember which the ap was over so i paid BT.
Luckily i usually plan for the next car so had the funds in my account, but in your case it being the first car on the scheme sometimes that could be an issue to get together.
You may have to call their bluff and say that you cannot do it as you do not have the funds and that’s why you want to use a cc. I’m assuming that might be the case as often the ap can be quite a sum of money
It might be just you want to gain some reward points or like me take advantage of 0% over two years.
Really it don’t matter all that really matter is what you thinks best for you and are they going to lose the sale over it. I doubt it, but they could do if it is company policy. I guess it depends if you have the ap available or not. If you don’t then you cannot pay the ap.
The other issue might be that as some have said it’s not cleared and the ap they taking is on the behalf of motability.