They won't have to pay the screen price, but they are trying to get you to, as it's not the most attractive deal for them.
As it is you will pay them £1500 to change. Out of that money they will have to cover the transport, preparation costs, VAT on any profit, etc, so it won't leave them with a lot. On top of that, they won't have all the money back that they will have had to pay for the new car, until they have sold yours. That could well sit on their forecourt depreciating by £200 a month over the winter. If you were having finance they might be a bit more accommodating as they could make some more money on commission.
You may get a better deal if you take the cash back for your car, get dripped up for £10k, then settle it after the first month (don't tell them the last bit obviously) Other than that, it seems you'll have to pay the asking price, or find another car.