Interest charged by HMRC owing to their delays?

I believe I underpaid tax on two SA returns before 2021. I wrote to HMRC by registered post 12 months ago offering the underpayment and asking for the entries to be raised on my SA account. I have had no response. I chase every 30 days by web-chat, to be told HMRC has my letter but there is a backlog and I can expect a reply within the next 30 days. When each 30 day period expires without a response, I chase again. I expect to pay late payment interest until the time I notified HMRC of the problem, but would HMRC try to charge interest for the 12 months my payment offer has been in the backlog queue?

Hi Sheffield Park,
I apologise for the delay in the reply to your letter.
If a Self Assessment is needed and once processed interest is charged then you can object to the interest charges once the balance the interest is charged on has been paid in full.
You can object in writing to
HMRC,
Self Assessment & PAYE,
BX9 1AS
UK
Thank you.