If it's from a dealer, they usually knock a bit off if you aren't trading anything in.
You might get lucky, but I doubt it, the price is the price these days, few will knock anything off unless it has sat around a while or been returned by another buyer. bare in mind anything you buy now is at the top of the market, prices are insane, but it will have a correction at some point, Sonner than most think,
A big Ford agent we do work for have survived on used cars for a while, but are not buying anymore and have reduced all stock cars to shift them, they have had a large delivery of new cars.
You are also wrong to think no part ex is to your advantage, part ex cars make dealers a good living, trust me, they want your part ex, even if it is not a retail car, you want your new car so will often take whatever they offer, there are traders who snap up the ones they cannot retail and pay a profit for them.
Often a late retail car will make more than the car you bought, and it is stock that comes to them.
We buy any car will be aware the correction is coming, so at the moment will low ball, it is Cinch that they sell them through, or put them through auction, 800 quid is a low figure on their expectations per car, it is more like 1500, those they retail through Cinch, more like 3k.
The dealer you are buying from quite likely paid way over the webuyanycar price at auction or as a part exchange, as said has to pay vat, give a minimum 3 month warranty, prep the car to retail ready, pay rent and rates, power and staff and cars are hard to find because of British Car Auctions, who own webuyanycar and Cinch trying to dictate the market.
Good luck with haggling, always worth a try, but if it is a car you want, do not waste too much time on it, finding another might not be so easy. At the moment it is still a sellers market.