In my view this is all down to whether the dealer is decent or not. In this case the answer is not. To buy a car, even an older one, and have it unfit for purpose after 40 miles - what's that, less than an hours use out of a £1,000 purchase? Unacceptable.
I bought an 11 year old Audi A4 a few years back after my Mazda 323 finally died - which I'd bought as a 10 year old car 8 years earlier incidentally. Got the Audi for a good price, it was a nice car. However, while I was getting used to it I noticed it'd cough slightly every so often and didn't go so well when pushing on. Additionally the economy was pretty poor - something a test drive (unless over an extended period) can't really tell you. With the help of a mate who had the VAGCOM software and lead, I traced it down to a lambda sensor failing. Reported this to the garage, they apologised, had the car in right away, sorted the fault free of charge and I kept the car for a couple of years of happy driving.
So, a cheap (£1,300), old car I'd bought had a fault. I got an instant apology and a very quick repair. No drama, no hassle, exactly how it should be in my view. Car developed no other faults during my ownership as the selling garage had made sure it was ok, lambda fault aside. So, there ARE of course good guys out there, it's just the odd t*sser that damages the reputations of all sadly.
OP: I really hope this gets resolved in your favour - I'm sure it will - however it'll doubtless take time and effort due to this COWBOY car dealers attitude.
As an aside, my soon to be 16 year old Impreza still goes just fine and passed it's last MOT without issue. Little bit of rust appearing, but other than that it's good - all electrics etc. are fine, it runs perfectly. It'll make a great car for someone if I ever sell it.
Scoob.