Last month I experienced the same thing from a number of alfa and non alfa dealers offered around £12k for my 07/56 23k miles Brera 3.2 Q4. Furstrated by it I advertised it privately and sold to the first viewer within a week at the £15k asking price and got 10 more calls after the the car was sold. If you don't mind the trouble of selling I suggest you go the private route - for me it was the easiest sale ever!
Someone out there must appreciate your car especially during the summer time, and you only need one buyer, unfortunately the dealers are fixed in their profit margin and not prepared to improve the PX offer. The £3k difference contirbuted towards its replacement budget and the bargaining power strengthend due to the cash buyer position.