I bought a secondhand car two months ago - is the seller responsible for fixing its faults?

My dad purchased me a 2009 MINI about two months ago, in which time I've done 2000 miles. When the car went for it's MoT, it passed with a minor refusal for headlight bulb but was advised an engine management light. I took it to Arnold Clark, who advised me the following: worn crank seal, worn vacuum pump seal, worn timing chain worn, worn campshaft defaiser pulley inlet/exhaust, leaking radiator and leaking aircon condenser. We have forwarded this report to the trader, but they're denying any responsibility because they say the vehicle passed a PDI inspection. They are also stating that the MoT was carried out with no problem, despite the MoT not checking all these issues. Can you advise where I stand in order to move forward? I have been quoted £3000 for the above work.
The 'supplier' is liable for any significant faults present or developing on date of sale and remains liable for six months. But how much of your list he is liable for depends on what is "reasonable" for an eight year old, second hand car - bearing in mind the price you paid. See: www.honestjohn.co.uk/faq/consumer-rights/ You have to take it to him first. He does not have to pay for the work to be done. Instead he could choose to buy the car back.
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