But the under what law a credit card company can ask money from a trader where the transaction never took place?? Credit card companies are not courts and they just can't claim money back what was never spent.
If BA is not going to pay back the miles and the OP is within the T&C only the court can force BA to return the mile. The only time any court would ask BA to pay actual money if the miles cannot returned (ie. BA closed the OP account, etc)
It can go very messy if you try to convert miles to money as one can argue over the actual value.
So OP give a call to BA, then a recorded letter, then court action if you are absolutely sure you can prove what you are saying. (I'm sure you can if you have the email, etc)