Don't know sorry, all overseas, different countries.

Details on the transactions would help determine why the Bank is saying they aren't fraud.  

I'm very familiar with the process around this. I don't think it's too dissimilar to any other bank. I'll try give as much general information as possible, given this is outside of official channels.

If someone calls through saying they've not made charges showing on their card, the process is pretty standard. It'll always be at least block, if not cancel + replace the card to be cautious, unless they can confirm that the charges were actually authorized and the cardholder just didn't recognize the name (common with ezidebit, debitsuccess etc, often just a gym membership).

A frontline CSR is not in a position to determine whether or not a charge is fraud or not, again unless they can establish with the customer that it's just company name confusion. If the charges are totally unrecognised, it goes to the Fraud and Security team. If the cardholder say for example, cancelled a membership and was still receiving charges, or didn't get the product, i.e they know the merchant, that's a chargeback. By your description it sounds like one for Fraud and Security, and there is zero reason a frontline CSR would not put it through to them after your first call, so that's a little confusing. You've had some replies regarding a form, but that's a discontinued process, it's all done by phone now. A police report is only required if the physical card is stolen, or someone with access to the physical card made the charges (essentially stealing the card info)

Also don't go to branches about this stuff, it's not their area.

It's possible I misread it, and it was investigated by Fraud and Security or Chargebacks, and they're the ones who have advised it's not fraud? I'm only vaguely familiar with the investigation process so can't really provide much help there I'm afraid. If I were you, I'd call and ask if it has actually been investigated by Fraud and Security/Chargebacks or not. There should be clear notes, or the CSR can just go through to those teams to check. You can even reach the Chargebacks team directly on 0800 732 392, so maybe give that a go.