You do have rights under the Consumer Rights Act 2015. This means that the vehicle must be of satisfactory quality, fit for purpose and as described. If what you’ve bought doesn’t satisfy any one of these three criteria, you have a claim under the Consumer Rights Act.
You have a legal right to reject goods that are of unsatisfactory quality, unfit for purpose or not as described, and get a full refund - as long as this is done within 30 days.
After 30 days, you will not be legally entitled to a full refund, but you will be entitled to have the car repaired or replaced, and if this cannot be done, then you will be entitled to a full refund, or a partial refund if you wish to keep it. The only exception to this rule is motor vehicles, where they may make a reasonable reduction for the use you've already had of the vehicle after the first 30 days.
If the car was faulty within the first 6 months, it is presumed to have been there since the time you took ownership of it. After 6 months, the onus will be on you to prove it was already there, which can be done by having an engineer inspect it.
I would suggest you put this to them, and if rejected then initiate a claim against them in the small claims court by visiting here https://www.gov.uk/make-court-claim-for-money
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