The Motor Ombudsman at
What are a consumer’s legal rights when buying a car? - The Motor Ombudsman lays things out quite clearly if you are outside the 30 day short term warranty time frame.
What they say is -
"If you are now outside of the first 30 days, the seller has one opportunity only to repair or replace the faulty car. You will not be able to ask for rejection at this stage.
This does not apply to cars purchased before 1 October 2015. The Sale of Goods Act allows the seller to either repair or replace the car within a reasonable period of time without causing significant inconvenience.
If you are complaining about a fault within the first six months of purchase, it is presumed this fault was there at the time of purchase. The seller will need to prove that this fault was not there at point of sale. If you are complaining about a fault outside of the first six months, you will need to prove that fault was there at point of sale.
If the seller is unable to repair the fault because the same fault persists or a new inherent fault has developed, or the replacement car has an inherent fault, then you can ask for your money back or a price reduction (partial refund) if you wish to keep the car.
Remember, for rejection outside of the first 30 days, the seller is entitled to deduct the mileage you have added onto the car."
If you require further clarification then call them. If you need to take legal action against the trader, then issuing proceedings is simple and not a major cost although costs can be claimed back if you win.
But you will also note, that the dealer can only deduct an amount for the mileage covered. They cannot claim for anything else