Thank you for the question. So the first thing I would advise (which I feel you may have done) is look through the T&Cs of the warranty an ensure that you were meant to be covered by this. If this is the case and the company are refusing to pay out, there is a process you need to go through prior to legal action. In the first instance you must exhaust the complaints procedure with the warranty company. If you do not obtain remedy from them, or they refuse to engage then you can escalate the claim to the consumer ombudsman. If you exhaust this and still do not have a remedy then at this point you can take court action and either recover the costs of the repair you have outlaid, of you can make them repair it (or pay for a repair). If the car is not fit for purpose you could look at invoking your rights under the consumer rights act again the seller and let them dispute it with the warranty company.
Under the Consumer Rights Act, if you find the there is a fault with the item purchased then you can ask for a refund within 30 days, if you exceed 30 days but are under 6 months then you have to provide the seller to repair or replace the item, if they cannot do this then you can request a refund. If you notice the issues after 6 months then the onus is on you to prove that the issues were present at the time of purchase which can prove more difficult. However if the seller is not willing to comply with any of your rights under the Consumer Rights Act then you can enforce these by taking court action.
I will provide you with a helpful link which will allow you to find a solicitor near your local area who will be able to assist you with this matter.
I hope this information has helped. You can find a local solicitor who deals with this on the law society webpage which is;
If you require any help moving forward on this matter in the future, please do feel free to come back to us and I would be more than happy to assist.