thank you. If the seller is a dealer or selling cars profit as a business, then you will have rights under the consumer rights act 2015. In particular, sections 9 to 11 of that legislation provide respectively that the car must be off satisfactory quality, fit for purpose and as described. from what you say, the car is neither of satisfactory quality nor as described and depending upon the fault, may also not be fit for purpose.
If you can demonstrate the car does not conform with any of the above provisions, which from what you say, you can, then you can claim breach of contract on the basis that the dealer is in breach of one or more of the above provisions which are implied into your contract by the above statute.
Any fauults that occur within the first six months following purchase are automatically assumed to be the dealer's responsibility and you do not have to prove whether the fault is the dealer's responsibility. Rather, the dealer would have to prove that the fault was as a result of damage you have caused to the car to avoid any responsibility. In addition, during the first 30 days, you are entitled to reject the vehicle if it develops a fault and demand a full refund.
In terms of how you may proceed from here, you can contact the dealer in writing-for example by email or if you prefer post, and send a notice setting out the fault or faults that are present in the car and advising that you are exercising your right to reject under sections 20 and 22 of the consumer rights act 2015 as a consequence of false and demand a full refund and reserve your rights in relation to any costs you incur as a result, for example if there is no delay in providing a refund, you need to secure alternative transportation which may include taxis or a rental car, providing that such costs should not be excessive.
If the dealer refuses to refund you, because you did not make an element of payment from what you say by credit or debit card, you would need to consider initially threatening and latterly actually issuing proceedings in the County Court to recover your monies. The simplest way to do so would be by using the following link: