Many thanks for your patience. When a person buys a second-hand vehicle from a dealer they will have certain rights under consumer laws, namely that it must be of satisfactory quality, fit for purpose and match its description. If the car does not satisfy any of these, the dealer will be responsible.
They will only be liable for faults that were present at the time the vehicle was sold, even if they become apparent later on. However, they will not be liable for fair wear and tear, misuse or accidental damage or any issues that were brought to the buyer’s attention before the sale. The age and value of the vehicle will also be relevant and the expectations of older vehicles will certainly be lower.
As you are too late to reject the car for a refund, all you can ask for is request that it is repaired or replaced without causing you significant inconvenience. The dealer may only reject a repair or replacement if it is impossible or disproportionate in the circumstances. If that happens, you are entitled to get it repaired elsewhere and claim back the repair costs, although there is an obvious risk in doing so as there is no guarantee in getting any of the money back.
If the dealer refuses to resolve this issue or accept any liability, you could take legal action against them. However, before going down that route you should try and resolve the issue directly with them by sending them a formal letter specifying how you want this matter resolved and giving them 7 days to respond. Advise them that if they fail to get back to you or deal with this in a satisfactory manner, you will have no other option but to report them to Trading Standards and issue legal proceedings to seek compensation.
This is your basic legal position. I have more detailed advice for you in terms of the steps you need to follow should you have to take this further, which I wish to discuss so please take a second to leave a positive rating for the service so far (by selecting 3, 4 or 5 stars) and I can continue with that and answer any further questions you may have. Don’t worry, there is no extra cost and leaving a rating will not close the question and we can continue this discussion. Thank you