Declaring savings interest

If my personal allowance is used up by my pension, and I have savings generating interest over £1000 do I need to declare that somewhere or is it automatically taxed by the tax office?

Hi 
The banks and building societies submit the untaxed interest details to HMRC after the tax year end.
Once received we will review the tax year and if underpaid a calculation will be issued with the details. 
Thank you.