Had you taken a pay cut in the lead up to your employer going bust? I may be wrong, but I think I was told once that if you take a pay cut to help your employer out when they just can't afford it, HMRC will tax the employer on the basis of what you should have been earning, rather than what you were.
Clearly none of that is your fault - you have a P45 and payslips that agrees to the amounts you've received, but it may explain how their system is showing something different than what you've provided.
Write to them again, provide copies of all your payslips, your P45, and maybe redacted copies of your bank statements showing that you've received the same amount as per your payslip.
If you're able to calculate your own tax liability, I would add:
"My calculations indicate that my tax and national insurance contributions for the period of my employment are £XXX, and consequently I calculate that a refund of £YYY is due to me. I can confirm that I have had no other earnings for the remainder of the tax year ended 5th April 2018.
I believe I have now provided all the information that you will need to process my refund, and would request that this is repaid to me in full, rather than adjusted via a future tax code.
As this matter has been dragging on since January, I would appreciate you attending to this as a matter of urgency."