Hi _viator,
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.
If the underpayment is less than £3000 and your PAYE income is large enough to collect the underpayment your tax code would be amended in the following tax year to collect.
We would use the untaxed interest figures supplied as an estimate going forward and your tax code would be adjusted.
f your untaxed interest changes you can contact HMRC to amend the code
Income Tax: general enquiries
Thank you.