Personal Savings Allowance, PAYE and UK Banks

I had understood that UK Banks advise HMRC about credit interest that been paid to individuals which is subject to UK Tax (so non ISAs) and we only have only have savings with UK Banks. We are both PAYE, but wanted to check if we needed to complete a self assessment due to the PSA . When completing the on-line tool to check if a self assessment was required it returned a result "You do not need to send a Self Assessment tax return" but also states "If you had untaxed income, You must tell HMRC between £1,000 and £2,500 in any other untaxed income, such as commission or money from renting out a property". I contacted HMRC via the 'Ask HMRC online' tool which gave links to what I'd already found and was not clear as to whether the savings interest should still be reported. It did state "You do not need to send a return for this. You can check your Income Tax and go to ‘Tell us about a change’" which I tried to do and it doesn't appear that HMRC have a record of my interest, yet I have been with the same bank all my working life (years!) and therefore I can't see interest having had any impact on my tax code. The Ask HMRC online tool, then gave further advice that would suggest I do need to complete a tax return "You must send a tax return if, in the last tax year (6 April to 5 April), you were earning untaxed income, including from savings, investments and dividends", which is conflicting advice to what my main bank advised... "Paying tax on savings interest - Banks and other financial institutions report all interest to HM Revenue & Customs (HMRC) at the end of each tax year. If you’re employed, or you receive a pension, HMRC may simply change your tax code, so interest is taxed automatically. If you complete a Self-Assessment Tax Return, you should report all earnings, including any interest earned on savings, before calculating and paying any tax due." Additionally our accounts are joint, so I assume that the amount of interest I would report would be 50% of the total for all accounts. Any clarity on this would be very much appreciated, I jst don't want to get this wrong by assuming.

Hi Nicki,
Unless your untaxed savings interest exceeds £10,000, you do not need to complete a Self Assessment return to declare this. Your banks and building societies will inform us of any interest automatically. If your total interest exceeds the allowances listed here - Tax on savings interest - the tax due will be collected through your code, or we will write to you with alternative ways of paying.
Thank you.