There are pros and cons to each method - private buying, or from a dealer.
When buying privately, it's sold as seen, so if anything major goes wrong there's no comeback. Major things don't really "just go wrong" on cars though, so you'd have to miss all the warning signs when looking over the car to put yourself in this boat. That's just about the only problem with buying privately, other than making sure the car is actually the sellers to sell, but HPI should see you over that hurdle. With a private seller, you get to see the car's owner, you can see how mechanically competent they are, how they drive it if they drive it for you, you can ask why they're selling it, speak directly to them about the service history etc...
When buying from a dealer you get the peace of mind from a warranty - but peace of mind is all it is. If the engine seizes down the end of the road for example you have some comeback, but for just about anything else (head gasket failure, a new clutch, braking system - all big £200-500+ jobs) you'll find that they're not covered by a warranty, so they're often not worth the paper they're written on. Car dealers are by and large, dodgy - they have to be, as not many cars are perfect, and they have to sell the ones that aren't. They have to make profits, and if they can possibly wangle out of paying for a warranty repair, they will. You can't meet the previous owner, will have no idea how they drove it, the dealer will often just have to say "I don't know, sorry" if you ask questions about the car's history. You're buying blind essentially.
Dealers are always more expensive, often a grand or so more (speaking £4k cars) than an equivalent car from a private seller. Given all the bonuses of buying from a private seller against all the downsides of a dealer purchase (given that warranty bonus is effectively null and void in 90% of cases), it does seem silly to buy a car this cheap from a private seller.
Only if I was spending £10k+ on a car would I choose to buy from a dealer - given that you have the added security of dealing with a registered business with a premesis when it comes to handling large sums of money, whereas a private seller could disappear off the face of the earth. For a £4k car though (which would be £3k in a private sale) it doesn't seem worth going to a dealer really.