Used Car Consumer Rights

Andy7777

I bought a used Skoda Fabia Automatic (2011) with ~40,000 miles on the clock - for about £5600. I bought it from an independent dealer, and it came with a 6 month RAC warranty. After 6 months and 2 weeks, just out of warranty, it developed problems with the automatic gearbox. Initially the dealer I bought it from was helpful, and offered to do some diagnostics on it, but they didn't have sufficient expertise to say what it was and suggested I take it to the Skoda dealer for diagnostics.
I was informed that the Automatic gearbox was shot, and that a replacement part would cost £4000 not including labour. Not only that, but also the timing chain was faulty and that would need replacing too. The total cost for parts and repairs would come to around £8000, beyond economic repair.
In the end Skoda agreed to pay 60% of the labour costs and all of the parts cost, but nothing toward the gearbox costs. This means that the car is still beyond economic repair.

Given the fact that I have had it for over 6 months, and the mileage is now 50,000 do I have any basis for a claim for costs against a) Skoda and b) The dealer I bought it from?

I did use my credit card to buy it also

Fosterdog

Have they said what could have possibly caused the faults? 10k miles in six months is a substantial amount of driving, could it be down to wear and tear rather than inherently faulty parts?