In reply to Del:
My tuppence
The fact he paid in instalments and therefore still owes money has no bearing on anything... bar making it harder for you to resolve.
In a normal transaction he would have paid and taken his car away. He would have had 3 happy weeks and then something would have gone wrong. He would have gone to garage and been told the car had a fault, or he's destroyed it in some way. Assuming the car had a pre-existing fault he would only have a very faint chance of recourse if you can be proved to have misrepresented the cars condition or deliberately covered something up. Which you state is not the case.
Even knowing there is a fault or potential for a fault would not be an issue legally (morally yes) if you didn't misrepresent things and if he didn't directly ask (simple example), you know there is bulge on a tyre that would require it to be replaced but you say nothing in the advert about tyre condition and he does not ask anything about tyre condition - if he fails to spot the issue and/or doesn't directly ask 'do the tyres all meet minimum legal standard' or 'is the car safe and is everything working and legal to the best of your knowledge' it would still be his problem. He would only have recourse if he could prove that you knew about something and lied.
The guy is being a dick. The lack of clarity on what the issue actually is seems a big red flag to me for starters but even if he tells you what the problem is, if you had no knowledge of it, it is entirely his responsibility and he is very much in breach of an agreement to pay you the agreed value of the car. And that value does price in the fact that it is an old sports car, of dubious reliability that requires lots of TLC and is prone to expensive work requirements.
Slightly different but a few years back I had a decent sum to spend on a fun car - choice was pretty much 2 or 3 year old Alfas, Audis, SAAB convertible etc - or similar spend on a ~12 year old Maserati - a friend with a one year old Masser advised me that he wouldn't touch the old one with a bargepole as it was a binary outcome... spend 10 to 15 grand and probably have it blow up in a year and be worthless, or at best have a multi thousand pound bill to get the car back to being worth similar to what it was when bought, with a strong chance of another huge bill just round the corner for whatever fails next. I went sensible as I couldn't bear to blow that much on one or two years 'fun'. Your car is not quite in that league but it's similar - older, performance vehicle of dubious reliability. It either goes well for a while or it goes horribly wrong... chances of getting a quiet few years out of it and a gently reducing value with minimal costs - pretty much nil. Buyer beware on second hand cars, even more so in the category described, even more so on private sale with virtually zero recourse on seller if anything goes wrong.
Sorry but only way I see this going is you write off the debt/come to a part arrangement and ultimately decide whether you want the guy as a mate or not or you file a small claims action (no expert but I understand this is relatively cheap and easy and I can not see any way you would not win) and definitely write the guy off. And make sure your circle of friends know the precise circumstances.
I suspect the guy is a chancer trying a fast one or one of lifes whingers who looks for an out/somebody to blame whenever something doesn't work out his way.... he shouldn't be leaning on a friend for sympathy or compensation. The legal bluster coming from him is nonsense and one hopes he will back down quick enough if you stand firm and if necessary raise a small claims action. Can't see somebody who needs to pay in lumps for a £2k car having much of a tolerance for legal fees to defend himself properly and even if he defends himself the facts seem pretty clearly staked in your favour whether the problem was pre-existing ort not. As stated, car just MOT'd (no guarantee of longevity but proof it was road legal when sold) and he test drove it and then ran it for 3 weeks without issue.