A couple of questions:
- Did the vendor knowingly mislead you as to the recorded mileage of the vehicle and did that materially influence your decision to purchase at the price you paid?
- Is the value of the vehicle materially different now that you know the "real" recorded mileage?
If the first statement is true then the vendor may have committed an offence and you may have a rememdy available in law. Whether that's worth pursuing is your decision.
If the second statement is true then it only becomes relevant when you come to sell the vehicle. Clearly you would commit an offence if you were to answer a direct question of "is the recorded mileage correct" in the affirmative as you know that not to be true. However, to answer the same question with "no, it has done more miles than are recorded but I don't know precisely how many more" is truthful.
FWIW, my view is that people get too hung up on recorded mileage and pay too little attention to the general condition of the vehicle. Once a car has done more than (say) 120k miles it all becomes a bit academic as the maintenance regime and vehicle condition has much greater influence on its value than what the odometer says. Personally, I wouldn't waste time and money getting the odo "corrected" to what, by definition, will be another incorrect recorded mileage. Personally, I'd be far more suspicious of someone who told me that they'd had the recorded mileage corrected unless they had some pretty good documentary evidence to support what it had been corrected to than someone who honestly said "it's done at least 10k more miles than recorded, but I don't know precisely how many".
If you're happy with the car then just drive it. If/when you want to sell it, advertise it at a price that its condition and maintenance record suggest is reasonable and don't make any statement you know to be false about the recorded mileage.