the mediation team i would have thought would tell the claimant seeing as theyve told you that the wrong entity has been chosen, to change this requires a judges permission, and/or a fee, so the case may fizzle out on its own accord, they might not want to spend twice on costs !
Your very best defense=
is you offered to repair the car, they refused.
they carried on using the vehicle thereby causing further damage.
its a 12 year old car
they have not contacted you before referring it to the court.
see if you can get it struck out on the basis of = 1 in wrong name 2 no contact before court action [ frowned upon by the courts letter before action] 3 pointless claim with poor evidence.
and if that doesnt work send a letter [ recorded] to the claimant explaining how you tried to help, no faults were present at time of sale, they refused to return the vehicle for you to repair it, and you are considering a counter claim against them for no more than a thousand pounds for your inconvenience, time spent replying to court action etc etc
and see if they drop it ..
