I have worked for several banks in the past. They do have a way to put you on their "do not call list" irregardless as to if you have a current account or not. You do have to contact them to have them turn off the choices. The banks should be able to turn off calls regarding any new lines of business and any "sister company" calls.

If you do have a current credit card with that bank and they are making an offer about that credit card, you will not be able to turn that option off. However, a different option would be to have them only be able to contact you by email. What I do is create an email account that I only use for solicitors and I give that email address out, however I rarely check that email account, but I can do it on my time, not necessarily when the email comes in.

Also about political calls, when you fill out your voter registration card and put your phone number on it the card, it is then given to the political party that you registered with. So if you do not want the calls to come, leave your phone number off the registration card.