Interest on personal savings - banks automatically report to HMRC

Hi there, I am an employee in the UK and accordingly pay tax via PAYE. I do not require to do a self assessment. It seems from what I can read online that banks automatically advise HMRC of bank accounts and of any interest made on savings. HMRC will consider if any tax is due and change the tax code accordingly to note and collect this. Is this correct? I do not need to do anything further? This is the same for all bank accounts across the UK?

Hi Katherine Trail,
Yes, the banks and building societies submit the untaxed interest details to HMRC after the tax year end.
Once received we will amend your tax code code and review the tax year and if underpaid a calculation will be issued with the details. 
Thank you. 
 

Thank you. In the case of a joint account presumably this will be noted by the banks / HMRC when making calculations (given I understand its 50/50). Thanks again.