When you open an account in Spain you have to show your Passport as you do in UK to prove identity. As a Non Resident you are not liable to pay tax in Spain so a Non Resident bank account is opened.
Two years from this date you will have to complete a Declaration stating your Non Resident status. All banks charge for this service and failure to send or hand in Declaration to your bank can result in your bank account being frozen.
Also when you renew your Passport you will have to take the replacement in to your bank so that they can take a note of your new number.
Your NIE will have your old passport number registered so ensure that you keep this passport should you need to show it as proof of identity. It may not be necessary but why take a chance.
This is Spain, whenever you think you have the correct amount of paperwork another copy is demanded. I saw a great clip once which showed someone finally getting one over on the beurocrats or jobsworth as they should be called.