The law states that up until 6 months after the sale of the vehicle, it's up to the dealer to prove that the fault wasn't there when he sold it to the purchaser. This is called the "Reversed Burden of Proof". They will know this and you can cite it to them if they claim "it's your fault"
If you have bought from a dealer in the course of his business then the Sale of Goods Act 1979 implies certain terms in to your contract with the dealer for the purchase of the car.
Go back to them, state that the car is not of a satisfactory quality under s14(2) of Sale of Goods Act 1979 and that you require that they repaired. They must do so within a reasonable time. If repair is not an adequate remedy then you can demand a replacement from them or refund if there is no adequate replacement.
If they refuse to make the repair or refuse to acknowledge the disrepair then you should state that you wish to deal with them only by way of written correspondence. Keep copies of everything. You will have to write to them stating either that they should make the repair within a stated time otherwise you will make an application to Court to recover the monies or that they should permit an independent professional to assess the state of the repair of the care.
If they are not compliant you should also tell them you will contact Trading Standards, http://www.tradingstandards.gov.uk/, and Retail Motor Industry Federation (if they are a member, http://www.rmif.co.uk/.
Once they know you are aware of your rights, dealers tend to be more constructive in resolving these things but if you need to litigate you can find litigation solicitors through the Law Society's website:-
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