Tax on interest from savings

Please can you confirm that, as an employee in the UK (paying tax through PAYE), UK banks inform HMRC of interest on savings, and so I do not need to do anything to ensure that I pay the correct tax on this interest? As I understand it, when HMRC receive the information from banks, they amend the tax code (if necessary) to ensure the correct tax is paid. I am not required to complete a self-assessment tax return. Please can you confirm that I need to take no action regarding paying tax on interest from savings?

Hi,
Your banks and building societies will automatically inform HMRC of any untaxed interest received after the end of the tax year. If you earn interest over your allowance but under £10,000 and are employed or receive a pension, HMRC will change your tax code so you pay the automatically.
The code for the current year will be based on how much interest you had in the previous year.
Further information can be found here:
Tax on savings interest
Thank you