Are you dealing directly with the other person? I would have thought the bank would be in the middle of any discussion.
Someone paid my husband's credit card bill once, I think the bank had the wrong account details logged for the Direct Debit. By the time I noticed (same day) and called the bank the other party had already alerted them and it was all put right immediatly.
That said, a friend of mine in the UK had £25,000 lodged to his account by accident and he had to pay it back.