This makes no sense from the dealer's point of view.

Putting that many miles on the car is almost bound to annoy the customer, and a BMW dealer cannot be short of cars to use.

It seems to me whoever did the miles cannot have realised the car was sold.

The fact the miles were done inadvertently doesn't alter the fact they were done.

Any legal argument would revolve around the difference in value between the car with or without the extra 600miles.

That's a difficult one, the extra miles will not have devalued the car by very much.

It will cost you money to attempt to prove the amount, and you may not succeed.

The dealer may argue there is little difference between the retail price of a car with 5,100miles or 5,700miles.

But good trading practice obliges the dealer to offer some form of compensation.

Practically, I think your best approach is to negotiate with them.

The miles cannot be undone, and you've already paid.

Getting any money back from the dealer is bound to be difficult.

I think you could reasonably ask for some free accessories, or a voucher for a service.