Help needed with tax code

Hi, I work for a teaching assistant agency so am paid on a weekly basis. I previously worked for a different agency but because they didn't send me a P45 before I started my new job, I've been put on an emergency tax code (200LX). I have been taxed at a really high rate for my first few weeks of work. My old job are being very slow to sort the P45. I just wanted to know if I have to send this P45 to HMRC or my new employer or if this automatically gets uploaded onto the system. Do I have to let HMRC know about any of this, and if so, how? They are proving very difficult to contact. Will I be refunded the money that was taxed too highly? Thanks

Hi 

Your previous employer will submit the P45 details to HMRC. Once received the tax code will be reviewed/updated.
Yes if overpaid you will receive the tax refund.
As the 2023/24 has just ended once the PAYE details are received your record will be reviewed and if overpaid a calculation will be issued to you with details of how to claim. 

Thank you