Seeking Help

I started a new employment in March 2024. I am entitled to tax free child-care, as my salary is below £100,000. My employer overpaid me in March 2024 (by mistakenly recording me as a full time, rather than part time, employee). The overpayment will be re-paid, likely in April 2024. The overpayment may artificially inflate my salary above £100,000 for 2023/24. HMRC advised that my employer can correct the tax position by submitting a Full Payment Submission/Earlier Year Update. My employer has informed me that they will not correct my P60 because income tax is calculated when a payment is made, rather than when it may or may not have been due. If not corrected, I am concerned that this means that (1) HMRC will consider that I am ineligible for support with childcare costs in 2024/25, and (2) it will appear to HMRC that I made a false income declaration re. my 2023/24 eligibility for support with childcare costs (potentially resulting in clawback). Please can you advise: (i) if my employer is taking the correct steps (including by saying that income tax is calculated when a payment is made rather than when it may or may not have been due), and if not, (ii) what I can do to encourage them to rectify my tax position. Thank you.