I’ve never really had an issue with HMRC details before. But I was on an emergency tax 2 months ago but since then my employer has corrected the tax code and they’ve been paying me under that tax code. However, HMRC still has the wrong tax code for me as BRX.
Do I need to do anything here? As in do I need to let them know to change it? Does it matter since my employer has the right tax code for me and I am paying the correct tax
Your employer communicates with HMRC around this, you don’t need to do anything 
thank you I thought as much, I thought they would update their records but it’s been two months and my HMRC app still says the old tax code
HMRC will pass the code through to your employer if your on PAYE.
If you think the code is incorrect you would need to speak to HMRC.
Your employer just follows what HMRC advise.
Your code means you will pay 20% on all earnings and won’t take into account any past income since 6th April.
HMRC usually communicate to you why they have changed your tax code.
Reach HMRC via web or app and get it change, I had this issue twice, first time they sent me a cheque because I paid too much tax(£650) and the second one, they changed my tax code so I paid less tax every month until next April.