Comment by TRiG_Ireland

It would be relatively easy to implement in Ireland, but I've only used it once (buying from a shop in Germany). I placed the order on their website, and they gave me an IBAN and a reference number. I did a bank transfer to that account using the reference number they gave me, and they marked the invoice as paid and shipped the product. Simple system, though I'm not sure how they monitored their bank account: it may have been manual. It would work for any company which uses IBANs, which is all SEPA companies and many more besides.

Australia has a system called POLi. This injects a popup into the checkout page of a website which allows you to log into your own bank and do a transfer from there. That works well, and seems quick and easy for the customer.