VAT is only paid once by the buyer (but not necessarily once by the seller - they will pay VAT on their profit margin in the resale via the "second hand margin scheme"), but the lack of it payable by the buyer on a second hand car is not the reason for the drop in p/x price offered should you change your mind days later, it is the margin in the car, the need of the dealership to make a profit on every car sold, whether that be new or p/x. A dealer will pretty much always look to make at least 15% on your p/x.
The dealer will always charge what they can for the car and always expect margin in the p/x, even if they made a killiing in the sale of the new one. If a pre-registered car (technically second-hand, VAT already paid) can be sold for RRP of the new one because the new one will take 6 months to order and supply (as some of the first Rs were), they will charge RRP and get it from someone choosing not to wait for the new one. VAT (or lack of it) does not dictate second hand prices at all.