got this from Which website
Returning a second-hand car
If there's a problem with a second-hand car soon after you've bought it - for example, the car develops a problem you wouldn't expect for the car's age and mileage, or it turns out not to be what you'd been led to expect - you may have the right to reject it and get your money back.
If you bought the car after 01 October, you only have 30 days to reject a second-hand car and get a full refund under the Consumer Rights Act.
If you bought the car before 01 October 2015, than you must reject the car within a reasonable time under the Sale of Goods Act.
While there's no clear definition of what a reasonable time is, it probably needs to be within three to four weeks – less if it's an obvious problem.
And if you reject a second-hand car you must stop using it immediately.
If you're past the first 30 days but a problem has become clear which would have been present at the point of purchase, then you're entitled to ask for a repair or replacement free of charge.
But after the first six months, the onus will be on you to prove that the fault was present from the day you purchased the car.
If the attempt at a repair or replacement is unsuccessful, you're entitled to a refund.
But the car dealer can make a deduction from the refund after the first 30 days for 'fair use'.
Second-hand car bought privately
You have fewer rights when you buy from a private seller and key parts of the Consumer Rights Act don't apply.
For example, there is no legal requirement for a car to be of satisfactory quality or fit for purpose.
But legally the seller must:
accurately describe the second-hand car (for example, an advert must not say 'one owner' when the car has had several)
not misrepresent the second-hand car (tell you something about the car which isn't true such as if it's been in an accident, the owner must answer truthfully).
was hoping this would be good news but looks like the consumer side is not covered