I presume you have an issue with the car or the finance agreement. The finance company owns the car here. You do have consumer rights which may have been breached if the car is faulty or if the finance agreement is unfair.
You are covered under the Consumer Rights Act 2015 here which means you have a right to expect a service (from the finance company) carried out with reasonable care and skill. Furthermore, the car should be “fit for purpose”, "free from defects" and “as described”. If it isn’t then you can allege breach of your consumer rights and breach of contract.
You should now make a formal complaint and if that does not resolve the matter ask them for a "deadlock letter", which is a letter giving their final response.
Once you have the deadlock letter the next step would be to escalate this to the Ombudsman - they will investigate and liaise with the finance company which would hopefully result in a refund. The finance company should arrange to return the car to the dealer if you want to reject it. They can order the finance company to make a financial award for inconvenience if they have acted poorly.
Once you have their final response, you can make the complaint here : www.financial-ombudsman.org.uk/consumers/how-to-complain
The Ombudsman will look at this case independently and will make a decision based on what happened. Their decision is binding on the finance company, but not you. So you would not be bound in law to follow their decision. If the Ombudsman did not find in your favour, therefore, you then have the option of suing the finance company for breach of your consumer rights and you have up to 6 years to bring a claim to the court (the limitation period is 6 years from your date of loss, to when you need to issue a claim).
You can also tell the garage you purchase the car from you are handing the car back (again, if this is your preference). If they agree then fine, this will speed up the process. If they disagree then you will have to make the complaint to the insurer and if that doesn't resolve matters, go to the Ombudsman. If you wanted a law firm to do the above, any of these could help you further :