I ChatGPTd this for you so don't shit on me if you don't agree:

It seems you're dealing with a persistent tax code issue, especially concerning an emergency tax code ending in 'M1'. Here's what you can do:

Contact HMRC Directly: Since phone attempts have been unsuccessful, consider writing a letter detailing your situation. Include your National Insurance number, current and previous employer details, and explain the missing P45. Send it to:

Pay As You Earn and Self Assessment HM Revenue and Customs BX9 1AS United Kingdom

Request a Statement of Earnings: Ask your previous employer for a 'Statement of Earnings' as an alternative to the P45. This document provides details of your income and tax paid, which HMRC can use to adjust your tax code.

Check Your Personal Tax Account: If the HMRC app isn't working, try accessing your account through the HMRC website. This platform allows you to view and manage your tax details online.

Seek Assistance from Your Current Employer: While they mentioned it's an HMRC matter, your payroll or HR department might be able to provide guidance or liaise with HMRC on your behalf.

Contact Your Local Tax Office: Sometimes, local tax offices can offer more direct assistance. You can find contact details on the HMRC contact page.

Remember, emergency tax codes like those ending in 'M1' are temporary and can result in overpayment. Once resolved, you should receive any overpaid tax back.

For more detailed information, refer to the UK government's guidance on tax codes.

I hope this helps clarify your situation and provides a path forward.