In law, the concept is of a fault that predates the time of sale. It would be reasonable in this case to assume that the battery was faulty prior to the customer collecting the car. The onus in these cases is for the dealer to show that the fault was
not pre-existing, not for the customer to prove that it was. Civil law requires the balance of probability to favour one side, rather than criminal law that requires beyond reasonable doubt. In this case, it is probable that the battery was on it's way out before the car was collected, as it would be extremely difficult to inflict enough battery punishment in 24 hours to destroy one.
Your third party warranty is irrelevant in this case. The dealer
must prove that this fault did not arise before you bought the car from them, which in practice is very difficult for them to do. At the least, reliance on an auction report is not defence, they must carry out PDI checks themselves.
Check your local trading standards & Citizens Advice. Under the Sale & Supply of Goods Act (Consumer Regulations 2002) any motor dealer must warrant their vehicles for 6 months from the date of sale. Note that in such instances the onus is on the dealer to prove that any fault arising was not preexisting the sale. Otherwise the seller is essentially liable. Explain this politely to your salesman, and give them enough time to redress the issue. Write letters, and send them recorded deleivery, retaining copies and postal receipts. If all else fails, you should explain to them that you will proceed via the Small Claims Track of the County Court, in respect to your expenses of a new battery, and incident costs in pursuing the matter with them. I'd be extremely surprised if they chance their arm on the possibility of a County Court judgement against them, which will cause issues if they broker finance on sales. More than likely the firm but polite approach will result in them reimbursing you for the battery.
When you buy a car from a dealer, the car must:
be of satisfactory quality
be fit for the purpose it's being used for, and
match its description.
Your rights are not affected by any breakdown insurance, guarantee or warranty you have. These offer you additional ways of sorting out problems but they do not take away a dealer’s responsibilities.
Have a read:
http://www.adviceguide.org.uk/index/your_world/consumer_affairs/buying_second_hand_vehicles.htm#you_bought_the_vehicle_from_a_dealerhttp://www.honestjohn.co.uk/forum/post/index.htm?t=52855