Claiming tax back following redundancy

I was made redundant in February and received no further salary in 2023-24. I was paying contributions through PAYE on a monthly basis however these payments were based on my annual salary expectation, which I did not fully earn due to ceasing employment before year-end. It is therefore my understanding that I have paid too much tax (as well as national insurance contributions). I have unfortunately realised too late that I should have completed a P50 form to obtain a refund straight away however as we are now in a new tax year the guidelines on the website say that if HMRC calculate an overpayment I will be sent a P800 form but this could take up to October 2024 to be generated. Can you please advise on how I can speed this calculation / repayment up? Please note: I am currently unemployed and using the redundancy payment and my savings to fund this period of unemployment. I need the overpayment back in order to contribute to this further. My redundancy payment was well within the tax free payment threshold. Many thanks

Hi,
There is not anything you can do to speed up the review as HMRC will review your record automatically once we receive your PAYE income details.
If you were in receipt of taxable benefits from your employer in 2023/24 this information is submitted on a form P11d with the deadline date 6 July. 
Thank you.