Think of a franchised dealer who sells secondhand cars as two different shops - new
shop and used
shop. The
shop selling new cars has decided to be the franchise for that make and, generally, all they sell is ordered in. If the car is available from the manufacturer's stlck then you get the new car pretty quickly, otherwise it takes some weeks. A part exhange is just part of thr payment. If a part exchange is taken in, the dealer then decides whether to resell it from the used car
shop, or whether to sell it on to the trade.
However if you approach the used car
shop to sell a car, the dealer will think how quickly he can sell the car, if at all. He will know his local market and will try and stock cars that he knows will appeal to the locals. I don't know Sidcup, but perhaps that isn't a place where high powered versions of family cars are popular. If, therefore, he had offered you a price, it would probably be
lower than he thought he could get at auction less his costs and a bit for profit. You would have felt as insulted as you felt when he refused to make an offer.