How does Tax on Savings Income Work?

Thanks! Your video was incredibly helpful. I have worked out that I WILL need to pay tax in this tax year because of increases to state-pension, small private pension and increased savings interest. The links you included are going to be helpful (I hope) as I am trying to find out why HMRC have started to take Tax from a Private Pension each month despite me not yet having submitted a Self-Assessment Form. I guess it's because they estimate what future tax might be though I don't understand how they can know if interest/bank rates will rise or fall! Thanks again!