Josie Scott-Taylor

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