Termination payment taxed incorrectly

Facts: I resigned from my job in early 2024. My employment contract states that I have 1 month PILON. As part my resignation negotiations I secured an additional 2 months of pay, which has been treated as an extention of my notice period (from 1 month to 3 months). I have been subject to full tax and deductions for the last 3 months of pay, as the entirety is now being treated as a PILON. Question: In my view, the above treatment is incorrect. As the additional payments were negotiated as part of my departure, I understand that these should fall with in the GBP 30k tax exemption. The first month is a true PILON and should be taxed. My former employer disagrees with this view, as they are worried about their liability resulting from potential underpayment of tax. How can I resolve directly with HMRC?

Hi tax_geek_34,
Please have a look at the guidance here on the taxation of pay in lieu of notice.
EIM12975 - Termination payments and benefits: payments in lieu of notice (PILONs) and gardening leave: general
Thank you.