Reporting to your bank is probably the best thing you can do as they should be motivated to stop them.
Replying to the phising email is only likely to have your address added to a confirmed list of email addresses with real people on the other end of them. It will invite even more spam.
Surely the point is that these emails are not coming from these banks but from some fraudster purporting to represent the bank. I would say that there is little in the short term that the banks can actually do to stop them. I assume the banks request that customers report the fraudulent emails so that they can build up a picture of the activity and pass the information to the police.
Checkout the Irish Govenment's MakeITSecure website for details on Phishing at [broken link removed] and the Garda website for advise on online security at .
Finally you can also look at www.globalsecurityweek.com which ran a comprehensive awareness campaign last year on this topic.
There are also phishing emails supposedly coming from Barclay's Bank in UK, I've seen several in recent weeks. Reported to Barclay's but heard nothing back.