Tax on less than a full year state pension

I have a private teaching and small civil service pension. On Dec 3rd 2023 I started my state pension. Both of these together this year will be £1500 under my tax allowance, a fact confirmed on my personal tax account online which states I have zero tax to pay. Imagine my shock then when I had £80 tax taken from me in my January private pension! What justification have HMRC got for doing this. I work on a very tight personal budget and this has left me short this month. Blatantly not fair.

Hi Geoffrey,
If your pensions plus state pension will be less than your personal allowance £12570 then we can update your tax codes to split the personal allowance to cover your pension income. To do this you can update your estimated pay for your pensions on your personal tax account online or contact HMRC to review/update your tax codes Income Tax: general enquiries.
Thank you.