The reason that I ask how close to you he is geographically is that if you issue Small Claims Court proceedings against him they will be transferred to his local court which may not be particularly convenient for you. You just need to be aware of that.
In circumstances like this, the Sale of Goods Act does not apply to the Private sale of the vehicle. However the seller must not represent the vehicle and it appears that he has clearly misrepresented the car.
Assuming that you have evidence from an independent third party of exactly what is wrong with the car and how much it will cost to fix, and the fact that the mileage is much higher than was indicated you have a claim for compensation/damages.
You would actually be entitled to reject the car and a full refund but being entitled to it and getting it are two different things altogether. You are probably, after almost a month and a half too late now to reject the vehicle anyway. Your remedy is compensation/damages
From now on, I would put everything in writing. Tell the seller of what faults you have found and tell him that unless he agrees to take the car back and refund you in full, you will take him to the Small Claims Court for the cost of repairing the car and putting it back into the condition he described it as, the reduction in value based upon the misrepresented mileage and for car hire while the car is in for repair. That will probably come to more than you paid for the car!
I would tell him that you need him to agree to this within the next seven days (give him until a date and then there is no dispute when the seven day time limit runs out) failing which you will issue Small Claims Court proceedings without further notice.
If you doesn’t agree within that timescale, then you can issue Small Claims Court proceedings quickly and easily by following this link www.moneyclaim.gov.uk
If he had said words to the effect of, here is the car as far as I know it’s in good condition and as far as I know the mileage is genuine but do come and make your own mind up as I have not owned it since new, then you would have had no claim but as he made the comments and representations that he did, that does give you a good claim.
Make sure that you print the advert off the website because as you are aware, they do disappear after a few months.
I clarify anything?