I had a specific price I wanted to pay when I went into the dealer last month. I had a trade in which I would normally focus on trying to get the best price for, but being a cash buyer all that really mattered was my price to change.
I told the salesman I had a price in mind but did not reveal this when asked, instead telling him to give me his best price to do the deal. The car I was buying was brand new and expected him to be way off what I had in mind, so I was surprised when he initially came back with only 1 grand over.
I then told him my price and before I left he had got within £300 of what I wanted to pay.
I visited another dealer straight after and used the same method but the closest they could get was £1500 over what I wanted to pay.
I slept on it then phoned the first dealer the next day and said throw in a free first service and I'll do the deal.
Right up till pick up day I didn't know exactly how much he had discounted the new car, but with the knowledge of how much my trade in should be and how much discount was available via carwow, this is where I arrived at the figure I had in mind....and probably reducing it a bit in my head.

As it turned out the discounted price of the new car was actually better than anything on carwow, the cheapest of which I would have had a 600 mile round trip.
I was very pleased, was a very straightforward stress free experience......significantly helped by the fact that I was prepared to forget it if I wasn't entirely happy with the deal.
Regarding GAP....as above never buy from a dealer because they can cost hundreds of pounds more for the same cover. There are a few out there but I use Car2Cover. Cost £208 for 3 years Vehicle Replacement Insurance on my S3 Black Edition.