Yes you can spot them at £10k but I bet they don't last long unless they need a rebuild.
At that level of price, I reckon that pretty much any short-door car (ie before the galvanised chassis and stainless bulkhead/valances) is going to need a fair amount of work if it hasn't already been done.
If it's done a decent mileage then the bodywork will need looking at, and if it hasn't, then the mechanicals are likely to need a going-over.
I suppose it's possible that a car can have been owned for 20 years or so, been looked after by an assiduously careful owner, maintained in tip-top condition, and then put on the market at a rock-bottom price, but I can't see it as being very likely!