What procedures are available to find out the identity of a bank's customer?

We are acting for a Bank (Bank A) in a matter where a mistaken payment was taken from Bank A's customer and sent to a customer of another Bank (Bank B). The payment was meant to be made to another party however it was sent to Bank B's customer instead. Bank A was at fault in this regard. Bank A therefore reimbursed its customer for the mistaken payment. We, acting on behalf of Bank A, are now looking to recover the funds from Bank B's customer. Bank B will not, however, disclose the customer's identity without order of the court due to confidentiality reasons. We are therefore trying to distinguish what is the most appropriate way to find out the identity of Bank B's customer.

The immediate answer is to apply for a Norwich Pharmacal Order (NPO) to order Bank B to disclose their customer's identity. The Banker's Books Evidence Act 1879, however, is specific to disclosure regarding Bank customers so this may also be relevant; does the 1879 Act extend to disclosing a customer's identity or is it limited to accounts/statements/etc.? I also note that several sources say that NPOs can be used to find out the identity of a "wrongdoer", however in this case, the mistaken payment was made due to Bank A's mistake; will the use of the word "wrongdoer" limit our ability to apply for an NPO? Can you advise what would be the most appropriate approach to take (NPO or an order under the 1879 Act or other)?