Under the sales of goods act the dealer will have at least some responsibility for the car for 6 months. See the quote below from trading standards:
The onus is normally on you rather than the trader to prove a claim (that is, to prove that the vehicle is faulty in some way). However, the law states that if you are claiming repair, replacement, full or partial refund within the first six months of ownership, the onus is on the trader to prove that the vehicle was sold without faults when you bought it. This is called the 'reversed burden of proof'. After six months, the burden of proof reverts back to you to provide evidence to support your claim that the vehicle was faulty when it was sold.
Glad you're enjoying the car though and fingers crossed you won't have any problems anyway! :)