As with selling anything you do your homework and you get the best results. I would strongly suggest looking at a number of sites that will value your car, including Autotrader, We Buy Any Car, Motorway. Then armed with a price you know you’ll get (allow for WBAC to reduce the value due to condition, they’ll find something unless it’s completely immaculate) you can walk away from the dealer, sell it elsewhere and pay cash for the difference. If you choose to sell privately, you’ll get more but it will take more effort and you’ll have to deal with the potential for people to waste your time.
All wise words and I’ve sold a lot of cars privately for the reasons that you state. However, there seems to be a ‘sweet spot’ at the moment for selling to main dealers, due to the ridiculously high prices that they can command for used cars. It will obviously only work if you are selling them a car that they can sell on their forecourt (as I did) rather than send off to auction, but I honestly believe that had I sold my daughters old car privately I would have been several hundred pounds worse off. They gave me £100 more than the highest valuation I could find for a private sale and I saved myself around £300 in tyres and repairs that I would have needed to have done to sell the car at that price. Then, of course, all buyers will haggle over the price. Reckon I was probably £400-£500 up against selling it privately, which has never been my experience before, and probably won’t be again!