Paying Tax on Interest

Hi, I received £1030 of interest in a savings account on the 31st Dec. As I understand it, I will need to pay tax on interest over £1000. However, the wording here (https://www.gov.uk/apply-tax-free-interest-on-savings) has me a little confused. I am employed, so "HMRC will change your tax code so you pay the tax automatically". It goes on to say: "To decide your tax code, HMRC will estimate how much interest you’ll get in the current year by looking at how much you got the previous year." Is this something HMRC does automatically? Perhaps informed by the bank? Or is this something I will need to declare to HMRC myself? Thanks for your help.

Hi AAlistair,
The banks and buliding societies send HMRC the untaxed interest details at the tax year end.
Once received HMRC will review the record and if underpaid in tax you will be sent a calculaltion with the details.
The underpayment will normally be collected in the follwing tax years tax code so collected over 12 months. 
Thank you.