I would call the bank and explain that what has happened so far and you would like to dispute the transaction. I'm not sure if you have used UK credit cards or debit cards or cards abroad so rules and polices might differ, however your bank can sort this out relatively quickly especially you should have a cancellation email, etc. Other than that you can go to CEDR and ask their help. It's a straightforward case, clearly BA IT just can't process refunds automatically and someone also made a mistake not knowing the refund rules, etc. BA should able to sort it out themselves but I guess the usual issue, staff not properly trained.