Copied and pasted from here:www.mumsnet.com/Talk/cars/1690297-Negotiating-a-Private-Sale
If the seller hasn't added 10% on to the asking price they're not doing it right. There are loads of negotiation techniques and it depends how cheeky you want to be.
It helps to have a reason to back up why you want money off - is there something that might make the car unattractive to a buyer? Scratches, worn interior, anything that can make you suck air through your teeth in your best plumber impression.
Full service history - if it doesn't have any then the car's potentially unreliable - knock money off; full service history and a ring binder full of receipts? Car is expensive to run - knock money off.
Tyres/brake pads getting low, need replacing soon - knock money off. Something rattles in the engine - "it's a bit of a gamble mate, but I'll give you £xxx." If you're going to knock something off, having a reason to do so makes them squirm a bit and less likely to just say "no."
Now, cheekiness level - 10% off should be standard, I would think i.e. advertised at £4400, they want £4K for it. If you're lucky they'll agree, but if they've got a modicum of nous they'll cut that back to at least halfway or more in their favour. Go in at 15-20% off if you've got your list of rusty arches and squeaky wheel bearings (as above).
Other things to factor in: do they want rid quickly? I recently got a car for about 15% under the asking price because they needed the space on the drive (first offer was accepted, wish I'd opened a bit lower!). Do they need the money? Are other potential buyers interested in the car?