Tax on savings Interest

Im an Employee on PAYE and a Basic Rate Tax Payer. I have earned over £3k for the 23/24 Tax year in savings interest and have tax to pay on this. Is this collected by a tax code adjustment next year and do I have to notify HMRC ? Can this be paid through Self Assessment if I wish?

Hi GS Kilmore,
Your allowances for earning interest before you have to pay tax on it include:
your Personal Allowance
starting rate for savings
Personal Savings Allowance
Please see the guidance at: Tax on savings interest.
for more information. Your options if you exceed your allowances are also covered here.
Thank you.