Buying second hand car privately ?

Not all car dealers are cocks – I could name you three in Derbyshire who I’d have no trouble recommending.

But you wouldn’t dispute the dodgy reputation is generally justified?

Yes – but I imagine it’s very dependent on where you live.

And especially at the sub £2k price point. But any sub £2k is a punt anyway, private or from a dealer.

You have no rights beyond the car having to be roadworthy and it actually being theirs to sell.

I think it would be unwise to assume even this in practice – vehicles are usually ‘sold as seen’. One needs to do one’s homework to decide whether the car is roadworthy or not (e.g. get a specialist inspection) and whether the seller is who they say they are, and actually own the car being sold. If any of these prove not to be the case after parting with the money, you’d probably end up having to take the individual to court (assuming you can ever find them again) which wouldn’t be cheap.

Of course.  Plenty of things aren’t lawful but still happen.