Hi NMM,
Yes, if you reach the higher rate tax band then the personal savings allowance is reduced to £500.
The banks do submit the interest details to HMRC at the tax year end and once we review if you have underpaid this will be collected in the following tax years code.
If you want to pay the underpayment instead you contact HMRC once the calculation is received we can advise of your options.
Income Tax: general enquiries
Thank you.