I view private sales (and selling privately) as an EPIC waste of time. If finances allow, buy the car from a 'reputable' dealership/group. This gives you buyer protection, warranty and many other things that a private deals do not with the beauty that it takes less time.
First car: MR2 Roadster, bought 2nd hand from Toyota Main Dealer.
Sold via auction company.
Second car: Lotus Elise SC, bought ex-dealer owned from Lotus Main Dealer.
Part-ex'd.
Third car: BMW 135, bought brand new from BMW Main Dealer.
For the correct deal/price, I would travel ANYWHERE in the UK as I did for the Lotus.