Interest savings NS & I

As I understand it you do not need to declare interest on savings below £10,000. Any interest you receive will be taxed through your code based on interest sent directly from the banks and building societies (subject to your £1000 tax allowance.) I have been told by N S & I that they do not inform HMRC of interest on their accounts. How are those who are not completing a SA tax return get taxed on any interest from these accounts?

Hi STELOUhm21*,
It is your responsibility to notify HMRC of any bank or building society interest that you are paid.
You can do this in writing or by telephone, providing details of your bank or building society name, sort code, account number, name of bank or building society, the untaxed interest amount and your individual share of interest from any joint accounts.
You can also do this if we send a Self Assessment tax return, forms P810, P161 or R40. 
Thank you.