Incorrect P11D has not been updated

TLDR: How long does it take for a corected P11D form to be recognised by HMRC? ................. My employer (who I left a year ago) has submitteed the incorrect P11D form for 2023-24. Brecause of this, HMRC is charging me an extra £350 in tax. I brought it up to my employer 2 months ago. They admitted it was their error and claim they have updated it, but sent me no proof of the update. I've checked on the status of my tax online and it still says I owe £350 because of that P11D form. I called HMRC and they say the P11D was never updated. The last record they have of it is 4 months ago (with the incorrect details). I've gone back to my employer and asked them to follow this up. Question: How long does it take for HMRC to see the updated P11D form? Surely no more than a few weeks right? I'm not sure if this is just a slow system, or if my employer/HMRC have messed up.

UPDATE! My employer has sent me the email confirmation that they updated the P11D form 2 months ago. The email confirmation came with a submission reference code. I tried to give this to HMRC as proof but they say they cant check the submission reference code because changes happen autoatically. HMRC still claims the P11D has not been updated, despite the fact that i can see from the email confirmation that it WAS updated. What can I do?

Hi,
We are not able to give a timescale for amendments being completed due to a large number of amendments that have been submitted.
Thank you.