You're happy with the car. Now comes the tricky bit: closing the deal.
Negotiating a private purchase can be a trickier than sitting opposite a trained car salesperson in a showroom. Most private sellers are just like you: a bit nervous, anxious to get a result, but likely to take a low offer badly.
If the car is reasonably priced, just make allowances for faults you've found. Back this up with costs from a dealer or car repairer. Come in with a slightly lower offer than you expect to pay. The seller may accept it or haggle for a couple of hundred pounds more. If he refuses to budge and says he's got someone else who's interested, fine. Leave your phone number and say you'll think it over. He'll come back to you if he's bluffing.
If the car is overpriced, say so. Quote our used car prices or show the seller other similar cars advertised at lower prices.
Once a price is agreed, offer a small deposit to hold the car while you get your finances sorted. Ask for a receipt for this. Also ask the seller to provide a 'bill of sale' for you.
It's safest to pay by cheque or bank draft: the money and payee can be traced if the deal goes wrong. You'll have to wait for funds to clear before collecting the car, the keys and all the relevant documents. Remember to arrange insurance in advance, and to fill in and send off your portion of the V5 registration document.