HMRC missing payment evidence

3 years ago I made a payment from my account to cover a tax bill for my wife. HMRC have now been in touch stating they did not receive this. I can see the transaction on my online bank account and now have a physical copy of the statement, which both show the payment being made to HMRC Shipley. HMRC claim there is nothing on their system suggesting a payment was made but I am fairly sure I paid using the online payment system. Unfortunately, I cannot see the details of the payment on my bank account. I have requested this but the bank have stated they may no longer have this information. I'm unclear what I can do as HMRC are denying receiving the payment despite me being able to see it. I don't understand why they have waited more than 3 years to follow up on this. What are the next steps?

Hi Ciaran Murdoch,
If you can see the payment on your online account, you may have enough information about that payment for us to trace it for you.
Your wife can contact us by webchat or post here:
Income Tax: general enquiries
For us to access her record and begin tracing the payment. 
Thank you.