Missing personal tax records, emergency tax code and formal complaint

Hello community, I have been facing 20% tax deductions for 5 months since I started my current employment. Initially that was about emergency tax code that supposed to be updated. I managed to call HMRC on 5th of January and since then my personal account shows correct tax code however my employer haven't notified at all, therefore my income falls below living wage. Additionally my personal tax account does not show any income or tax deductions. I have contacted HR department and they keeps claiming and that all my payroll data has been submitted correctly and it need to be resolved by HMRC. I called HMRC again and have been told that this looks like very common payroll mistake that suppose to be sorted by my employer. With correct personal tax records I would expect to get it sorted straight after the end of current tax year. But for now seems like nothing gonna change, therefore I have to consider formal complaint and legal steps. Both sides refuse to take responsibility and I'm desperately seeking help. I'm going to send a formal complaint, as informal disputes does not help at all. Please advice if I suppose to submit complaint to my employer or HMRC? Kind regards, 

Name removed admin .

Hi Dawid Ryszewski,
I am sorry your tax code has not yet been amended.
To submit a complaint online about HMRC you need to go toComplain about HMRC
Select complain online if you're an individual or a business.
To write the address is:-
PAYE & Self Assessment Complaints,
HM Revenue & Customs,
BX9 1AB.
If you have a dispute with your employer you will need to contact ACAS, Advisory Conciliation and Arbitration Service, www.acas.org.uk 0300 123 1100 Monday to Friday 8am to 6pm
Thank you.