Recently bought a car with cash and you're right, in general getting discounts seems to have gone out the window. They definitely prefer selling PCP/HP, and when you do the maths its easy to see why.
Most blamed the fact that with all cars being online, they naturally have to price aggressively to get sales and as such are not willing to go lower or even discuss haggling.
My advice would be spend a good amount of time researching on autotrader/motors.com looking at the models you're interested in and you'll quickly come to know what price they sell for, then you'll know whether it's actually fair to try and haggle the price down or whether the price is already just worth paying.
The company I got mine from said they couldn't knock the price down, but as I was part exchanging would give me more for my car - they actually offered me about 60% more than any other offer I'd had for my car and stuck true to that offer when they saw the car which I wasn't expecting. Maybe that could be something you could ask for if you're part exchanging.
