It depends what you have to part exchange. If you have a car worth £15k, the dealer won't get all of his money until he's sold that (most probably having to take a px against that too), so you are less likely to get as much of a discount.
If you are going in with cash, it's a case of he's got the car, you've got the money, do a deal and go home. My Golf was £17,495 on the screen and I paid £16,200 for it by having nothing to px.