I had exactly the same problem, but the bank I was trying to join told me to contact the Tax Office and ask for a "Notice of Coding". They even gave me the exact number to ring, because it's not so easy to find just by googling. I rung the tax office, they sent the form, and I was able to join the bank. But the bank should have suggested this option in YOUR case. It worked for me, the tax people knew exactly what I wanted and why, because apparently it's quite a common request.