Savings interests, PAYE and self assessment

Dear Madam/Sir, I am in full-time employment. I pay income tax through PAYE and have never needed to complete a tax return. With interest rates increasing I may need to pay tax on interest from some of my savings for the first time. Am I right in thinking that my various banks will tell HMRC the amount of saving interest I've earned in the current tax year and HMRC will automatically update my tax code and the tax on interests will be paid automatically? ie I don't need to do anything? In this situation, I don't need to do a self assessment. Is this correct? Thank you very much.

Hi,

Please refer to link below for guidance:

Tax on savings interest

Thank you.