As said above. Research the value of your car (be realistic) & research the value of your potential purchase.
If poss, sell private.
Have a max figure you are willing to spend & stick with it.
It's the cost to change that matters & not what you want for your p/x.
If you've seen a vehicle & can wait until the 4th week in the month, you might have a better chance of a deal. (monthly target/sales figures)
I've bought a couple of times in the past just before Christmas & got decent deals.
I never tell the salesman up front what I'm willing to spend, but they have a rough idea by the car you're enquiring about.
As negotiations/conversation goes on, they will need some idea of your budget, so I tell them I'm looking at spending X £'s (less at least 15%)
If they flatly refuse, you can be fairly certain there won't be a deal at that price.
I'll then up my offer by maybe 5% & say that is my max.
Off they pop to see their manager.............

on return it's nearly always " we're getting there, but not near enough".
At this point i'll um & i'll ahh,.....then um & ahh again, shake my head a couple of times & say it doesn't look like i'll be able to afford it.

(silence then usually ensues for a few seconds)
I'll then offer another couple of %.
Again, off they pop to see their boss

............. on return saying "Ooooh we're nearly there!."
At that point I get up to walk, but say I can
maybe borrow a few quid from family, then offer another couple of %.
At that point it's usually enough.
If they let you walk out & don't ring you back within 24 hrs, your offer wasn't quite enough.
I've left showrooms/dealers over 6 months road tax...... but I've also had the phone call after being back home for an hour, that they'll do the deal.
It's a game & they're a business after all. Pity it's such a PITA & takes what seems forever, but it's your hard-earned.
Don't get fixated on that 1 car you've seen............there are others just as good (or better) if you can wait a few weeks.