Cut and pasted from the FAQ section of this site:

CONSUMER RIGHTS. How do I reject a duff car or get compensation for problems with a car I have bought from a dealer?

You have to invoke the Sale of Goods Act 1979 Part II Section 14, as modified by the Supply of Goods and Services Act 1982, subsequently modified by the Sale and Supply of Goods Act 1994, contending that the supplier is in breach of contract to you for supplying a car which was not "of satisfactory quality", or did not remain so for a reasonable period of time. Appeal Court Case law (Bernstein v Palmerston Motors 1987) has held that the supplier must be given three chances to rectify the fault for which the goods are rejected and must have failed to do so. The goods must be returned to the supplier together with all keys and paperwork. (Scott and Scott v Blade Motor Company 1997.) And the supplier (in the case of a car the dealer principal of the dealership) must be sent a letter by recorded delivery detailing why the car has been rejected as not "of satisfactory quality". Case law (Rogers v Parrish 1987) has put a limit of 6 months on the time you can successfully reject a car and obtain a full refund, though lesser refunds, taking account of mileage covered, may be obtained outside that period. The price you pay compared to market value will be taken into account. So if you buy a cheap car on trade terms you cannot reject it under the Act. And if you buy a cheap car (under £2,000) on retail terms from a trader, you cannot reasonably expect it to be perfect.

The Supreme Court verdict in Clegg v Olle Anderson (trading as Nordic Marine) 11-3-2003 has caused some confusion which some believe to have overruled Bernstein v Palmerston Motors 1987. In this case a yacht was supplied with an overweight keel in breach of its specification which formed part of the original contract. It was held that Clegg could reject the yacht at more than 6 months from date of purchase even though Mr Anderson had offered to make modifications to try to correct the fault. Basically, because the yacht had originally been supplied "of unsatisfactory quality" and this was admitted, Mr Clegg retained the right to reject it. For Clegg v Olle Anderson to apply to other cases, it must be proven that the fault existed on the date of sale and constituted a breach of the original purchase contract. Clegg v Olle Anderson cannot apply where a fault develops at some time after purchase. In those cases, Bernstein v Palmerston Motors 1987 still applies and the dealer has to be given three clear chances to rectify the problem.

The Supply of Goods to Consumers Regulations 2002, is derived from EU Directive 1999/44/EU which became Clauses 48A to 48F inclusive of the Sale of Goods act in April 2003. This reverses the burden of proof so that if goods go faulty within six months after purchase it is deemed they were faulty at the time of purchase and the trader has the onus of proving that the item is not defective due to a manufacturing defect.

Hi Matt,sorry to hear of your problems, but other than the failing to start I'm unsure what claims you have on the dealer

You see it is a used car & as such will not be in perfect condition, although many people buying BMW AUCs do think so (& I'm not saying this applies to you).

The questions need to be:

1. Did the car differ from the description? For example it obviously had imperfect bodywork when you saw it (you did see it, yes?) - did they promise to repair this or have you simply assumed they would?
2. Did they promise to replace the DVD headrests?
3. Did they promise you a certain volume of fuel?

If they have promised you all the things you want, then you clearly have a case; if they didn't then you don't.

However, being unable to start the car is a different matter. You have given them opportunity to fix it & it appears that they have done so; the fact that you do not believe it has been fixed is no grounds for rejection but if it breaks down again then yes (IMO) you have grounds to reject the car.

Clearly you are not satisfied with the car or the dealer & so my advice would be to approach BMW UK. They are very customer service orientated & very proud of their AUC.

Good luck