Employer not updating my tax code/financial hardship

Looking for some advice please guys. I joined a new employer on 1st November this year and brought with me a P45 that had an incorrect tax code of K242 from a previous employer which had resulted in a hefty overpayment of tax. I had called HRMC prior to starting at the new employer, they corrected the code and advised to call them again a couple of weeks in to the new employment with my company's PAYE reference and they would issue the company with a tax code notice.

I advised my employer on the first day of my employment of the issue and asked for their PAYE reference number. It took 9 days for the payroll lady to send it through. Once I had it, I called HRMC who said they had issued the new employer with a tax code notice, I received my paper version a couple of days later. After I had received the paper version, I sent payroll an email asking if the code had been received electronically, they didn't respond until 20th November saying it hadn't and we had now missed the deadline for the November pay run which meant I wouldn't be receiving my tax overpayment back and would be subject to another overpayment due to the K code still being in place. On that day, I still called HRMC to get another code notice sent out.

Not wishing to be an !!!! in my first month, I bit my tongue and managed to borrow some money in an attempt keep my head above water until the December pay run. When payroll emailed on the 20th November to advised they hadn't received the code, they told me to call HRMC on the 6th December to chase again. I decided I wasn't prepared to wait until the 6th and called after pay day on the 30th November and HRMC advised they would re-issue the notice and also advised they could fax it to my employer. I advised payroll of this and asked for the fax number without a response.

Obviously we are now into December and I started getting worried about how close we are getting to the pay run given we get paid early this month (22nd), so I contacted payroll again and asked if I could get HRMC to fax the code so we can ensure we had it sorted in time. They finally gave me the fax number so I called HRMC, typically their phone lines were down until yesterday afternoon, so the fax is being sent this morning. During the day yesterday, the HR Manager came up to me after I had copied her in to some emails with Payroll saying that I needed to be sympathetic to them and how busy they are etc. and that 'there are probably hundreds of other people in the company with the same problem.' Not particularly helpful when you are heavily in debt with Christmas looming and just trying to get people to do their jobs to fix a problem that is out of your control for the most part. The HR Manager then let slip that payroll for December has already been run so it would seem I again will not receive my rebate and will be overtaxed again. What I can't understand is why the payroll lady told me to call HRMC on the 6th December if she knew she was running payroll before then?

This morning I spoke to HRMC who confirmed the fax will go out this morning. The also confirmed that they sent electronic tax code notices on the 9th, 20th, 26th, 29th and 6th December. They also advised that employers have access to a Helpline which they can call to confirm employees' tax codes. If this is the case, why is my payroll department sitting waiting for 5 electronic notices to not be delivered (clearly an issue with their system) when an employee has raised an issue that is causing them financial hardship, that can seemingly be solved with a phone call?

The point to all this really is that I'm trying to understand where the fault lies here and what I can do about it. I currently don't have a car to get to work and, whilst I appreciate it's not my employer's duty to get me to and from work, I was going to use the tax rebate that the HRMC have advised I'll get once the correct code is used to buy a vehicle. As a result I've had to rent a car from 1st November through to 21st December (currently but now looks like I will need to continue until the January pay day assuming we get it sorted then!), which isn't a cheap thing to do! From researching, I believe the employer has a legal requirement to pay the employee using the most current tax code issued by HRMC, but I can't find anything official confirming this. I don't believe my employer has made a reasonable effort to ascertain the correct code despite me advising of the issue on my first day. They have a known issue with not receiving the codes electronically, didn't offer up the fax number when I asked and could have, very easily I find out, just have called the HRMC to get the correct code in time for the December pay run. I appreciate that most people will just say that I should think of it like a savings account and I know I will get it back eventually, but it has caused a lot of problems, unnecessary additional expenditure in the form of needing to rent a vehicle and I'm now on sleeping tablets due to the stress of it all.

I feel very aggrieved that I've raised an issue, done everything I can from my side to sort it but my new employer is not supporting me or fulfilling their duty to pay the correct tax. I've been made to feel like I'm bothering the payroll lady but I've been extremely respectful in all of my communications with her and tried to keep from pestering where possible. Is there any come back here or do I just have to wait until the payroll lady decides to pick up the phone to the HRMC or receives the fax. At the minute I am struggling not to just walk out! Any help/advice gratefully received.