Selling as an innocent private seller you not obliged to do anything unless you said it was genuine miles.
This.
It was a private sale. Therefore Caveat Emptor!
Unless you "Knowingly misrepresented the mileage" then your buyer has no comeback.
You can tell him without fear of redress that you honestly believed the car was "as it is." Jog On Kitty!
Up to you if you want to give a full refund as a matter of goodwill. This may be the best option as word gets around, and you don't want a dodgy rep in the motor trade.
